A Ph.D. dissertation is a significant and rigorous endeavor that requires a great deal of planning, research, and analysis. One of the most critical components of a Ph.D. dissertation is the statistical analysis. This section is crucial as it helps to establish the validity and reliability of the research findings. In this article, we will discuss the importance of statistical analysis in a Ph.D. dissertation, the types of statistical analysis commonly used, and the steps involved in conducting a statistical analysis.
The Importance of Statistical Analysis in a Ph.D. Dissertation
Ph.D. dissertation statistical analysis plays a crucial role in a Ph.D. dissertation as it helps to establish the validity and reliability of the research findings. This is particularly important in the social sciences and other fields where quantitative data is collected. The goal of statistical analysis is to draw inferences from the data, and this process requires the use of appropriate statistical techniques to ensure that the findings are accurate and unbiased. For example, statistical analysis can be used to test hypotheses, establish relationships between variables, and identify patterns in the data. This information can then be used to support or refute the research question, and it can also be used to develop new hypotheses for future research. In addition, statistical analysis allows researchers to make generalizations about the population based on the sample data collected.
Types of Statistical Analysis Commonly Used in Ph.D. Dissertations
There are several types of statistical analysis that are commonly used in Ph.D. dissertations. The most commonly used types of statistical analysis include:
- Descriptive Statistics: This type of statistical analysis is used to summarize the data and describe the characteristics of the sample. Descriptive statistics include measures such as mean, median, standard deviation, and frequency distribution.
- Inferential Statistics: This type of statistical analysis is used to make inferences about the population based on the sample data. Inferential statistics include techniques such as t-tests, ANOVA, and regression analysis.
- Non-parametric Statistics: This type of statistical analysis is used when the data does not meet the assumptions of parametric statistics. Non-parametric statistics include techniques such as chi-square, Wilcoxon rank-sum test, and the Kruskal-Wallis test.
- Multivariate Statistics: This type of statistical analysis is used to examine the relationships between multiple variables. Multivariate statistics include techniques such as factor analysis, principal component analysis, and multiple regression analysis.
Steps Involved in Conducting a Statistical Analysis in a Ph.D. Dissertation
The process of conducting Ph.D. dissertation statistical analysis in a Ph.D. dissertation involves several steps, including:
- Defining the research question: The first step in conducting a statistical analysis is to define the research question and determine what type of analysis is needed to answer the question.
- Collecting the data: Once the research question has been defined, the next step is to collect the data. This may involve conducting surveys, experiments, or other forms of data collection.
- Cleaning and organizing the data: After the data has been collected, it needs to be cleaned and organized. This may involve removing outliers, missing data, and other errors in the data.
- Analyzing the data: Once the data has been cleaned and organized, it can be analyzed using appropriate statistical techniques. This may involve conducting descriptive statistics, inferential statistics, non-parametric statistics, or multivariate statistics, depending on the research question.
- Interpreting the results: After the data has been analyzed, the results need to be interpreted. This involves identifying patterns in the data.
Ph.D. Thesis Analysis Using SPSS – How to Analyze Thesis Data
A Ph.D. thesis is a culmination of a student's research efforts and represents the most advanced level of academic accomplishment. As such, it is important to ensure that the data and analysis presented in a thesis is accurate and statistically sound. One tool that can be used to aid in this process is SPSS, or Statistical Package for the Social Sciences. SPSS is a software package that provides a wide range of statistical analysis tools, including descriptive statistics, inferential statistics, and data visualization. It is commonly used in the social sciences, as well as in other fields such as education, psychology, and business. One of the key advantages of Ph.D. thesis analysis using SPSS for analyzing data is its user-friendly interface. The software is relatively easy to navigate, even for those with limited statistical expertise. This allows students to focus on their research and analysis, rather than struggling with technical issues. Another advantage of using SPSS is its wide range of statistical analysis options. The software can be used to perform a variety of statistical tests, including t-tests, ANOVA, and regression analysis. This flexibility allows students to choose the most appropriate test for their data, rather than being limited by the capabilities of a single software package.
When using SPSS for data analysis in a Ph.D. thesis, it is important to ensure that the statistical tests used are appropriate for the data at hand. This includes ensuring that the data meets the assumptions of the test, such as normality and independence. It is also important to interpret the results of the analysis in light of the research question and the limitations of the data. Data visualization is also an important aspect of data analysis in a Ph.D. thesis. Ph.D. thesis analysis using SPSS provides a wide range of options for creating charts and graphs, including histograms, scatter plots, and line graphs. These visualizations can be used to clearly and effectively communicate the results of the analysis to the reader. In addition to the above, it is important to note that SPSS is highly customizable and flexible software. This means that it can be easily integrated with other tools and software, such as Excel or R, to perform more advanced analysis or visualization. Overall, SPSS is a powerful tool that can aid in the analysis of data in a Ph.D. thesis. Its user-friendly interface, wide range of statistical options, and data visualization capabilities make it a valuable tool for students and researchers. However, it is important to ensure that the statistical tests used are appropriate for the data at hand and that the results are interpreted in light of the research question and limitations of the data. In conclusion, SPSS is a powerful tool that can be used to analyze data in a Ph.D. thesis. Its user-friendly interface, wide range of statistical options, and data visualization capabilities make it a valuable tool for students and researchers. However, it is important to ensure that the statistical tests used are appropriate for the data at hand and that the results are interpreted in light of the research question and limitations of the data. With the help of SPSS, Ph.D. students can effectively analyze their data and present their findings in a clear and convincing manner.


A car is traveling at a speed of 48 miles per hour. What is the car's speed in miles per minute? How many miles will the car travel in 2 minutes? Do not round your answers.
To find the miles per minute from the miles per hour, divide the mph by 60 since there are 60 minutes in an hour. So if a car is driving 48 mph, divide 48 by 60 to get the miles per minute. If a car is driving at 48 mph, then the car's speed in miles per minute is .8 miles per minute.


Eugenia Cheng, author, musician, mathematician
Wed, Apr 5 7:00 PM (90 min)
Mathematics can be tasty! It’s a way of thinking, and not just about numbers. Through unexpectedly connected examples from music, juggling, and baking, Dr. Eugenia Cheng will demonstrate that math can be made fun and intriguing for all. Her interactive talk will feature hands-on activities, examples that everyone can relate to, and funny stories. She will present surprisingly high-level mathematics, including some advanced abstract algebra usually only seen by math majors and graduate students. There will be a distinct emphasis on edible examples.
David Fray, piano
Tue, May 9 7:30 PM (120 min)
After being named “Newcomer of the Year” in 2008 by the BBC Music Magazine, French pianist David Fray has embarked on an active career as a recitalist, soloist and chamber musician worldwide. Described as “perhaps the most inspired, certainly the most original Bach player of his generation,” with his natural elegance and exquisite musicality, Fray’s performance and skill must be experienced. Please join us for this exciting evening.


French Numbers: How to Count in French from 1-100+ Before Travel to France
Bonjour and welcome to your guide to learning French numbers! In this post, we will embark on an exciting journey to uncover the secrets of counting in French.
Whether you're a beginner or looking to brush up on your skills, this comprehensive guide will equip you with the knowledge to confidently navigate the world of French numerals.
From the fundamental digits to the more complex numbers extending beyond 100, we will explore each numerical milestone with clarity and precision.
Along the way, we'll also delve into the intricacies of French number pronunciation, ensuring that you not only understand the numbers but can also pronounce them fluently. Get ready to dive into the enchanting realm of French numbers and expand your linguistic horizons.
Before We Get Started
Learning French numbers is an essential skill for anyone planning to travel to France. Beyond just the practicality of everyday interactions, knowing how to count in French enhances your travel experience in numerous ways.
From understanding prices and currency exchanges to reading timetables for trains and buses, mastering French numbers empowers you to navigate with ease and confidence.
Ordering in cafes and restaurants becomes a delightful experience when you can effortlessly communicate quantities and make accurate transactions. Moreover, locals appreciate the effort made to speak their language, and it fosters a deeper cultural connection.
So, embrace the beauty of French numbers before your journey begins, and unlock a world of possibilities during your travels through the charming streets of France. Bon voyage!
Counting in French
The counting system in French is essentially split into three phases.
The first phase is the numbers 1-16; these give you a base for all other numbers. Once you have these memorized, the rest of the French numbers are simple variations of them.
Below, you will find a list of numbers 1 to 100, grouped together in singles, 10s, 20s, 30s, etc.
Each number will be written in the Arabic numeral system, (1,2,3, etc.), then in French. For the first twenty numbers and the first number of each set, I will spell out the French pronunciation of each number, so that you will know the correct way to say each one.
After you practice a bit, I highly recommend you look up videos or recordings of native speakers saying these numbers so that you can get the pronunciation down.
Now, let's start easy with the single-digit French numbers 1-9.
These first nine numbers are the foundation for understanding French numbers pronunciation and for learning how to write out larger numbers.
2 deux duh
3 trois twah
4 quatre kat-ruh
5 cinq sank
6 six sees
7 sept set
8 huit wheet
9 neuf nuhf
10 dix dees
11 onze onz
12 douze dooz
13 treize trez
14 quatorze kah-tohr-z
15 quinze cans
16 seize sez
From 17 to 69, you will use the tens number and add every single number on the end.
For example, below you will see that the number 17 is dix-sept, which literally means ten-seven.
Each of the below numbers in French will follow this rule up until number 69.
Once we get to number 70, you will see that things get a bit more complicated. For now, just focus on this rule.
17 dix-sept dees set
18 dix-huit dees wheet
19 dix-neuf dees nuhf
The 20s follow the same rule as the last three 10s except you sill replace dix with vingt or twenty. This will continue with the 30's, 40's, 50's and 60's.
20 vingt van
30 trente tront
40 quarante ka-ront
50 cinquante san-kont
60 soixante swa-sont
This is when things start to get a bit complicated.
Depending on where you visit, you may hear different types of numbers in French.
The reason for this is that in France, people use the numbers in the first column, which requires a bit of math.
Instead of just saying seventy-two, they say sixty-twelve, because sixty plus twelve is 72.
However, if you go to Belgium or Switzerland, you may encounter a different way of counting.
These countries chose not to use the mathematical technique and so the rules above continue to apply to the numbers above 69.
It is best to learn the France version of these French numbers first. Once you figure the math out, the other versions will be a breeze.
Given that it is not essential to learn these versions of the French numbers, the alternatives will only be listed next to each number in this set of 70s.
This way, you will get a glimpse of how it is different.
French Numbers in France Vs Belgium & Switzerland
70 soixante-dix (literally meaning sixty ten) swa-sont dees 70 __septante
71 soixante-onze 71 septante-et-un
72 soixante-douze (sixty twelve) 72 septante-deux
73 soixante-treize 73 septante-trois
73 soixante-quatorze 74 septante-quatre
75 soixante-quinze 75 septante-cinq
76 soixante-seize 76 septante-six
77 soixante-dix-sept 77 septante-sept
78 soixante-dix-huit 78 septante-huit
79 soixante-dix-neuf 79 septante-neuf
The grouping of eighties starts each number with quatre-vingt, which literally means four twenty because 80 = 4 x 20.
For this grouping, the following numbers will have the French word et in them, which just means and.
A lot of times there will be versions of numbers with et and without et. For this grouping, I have written both versions side-by-side.
80 quatre-vingts (literally meaning four twenties) kat-re van
81 quatre-vingt-et-un (or quatre vingt un)
82 quatre-vingt-et-deux (or quatre vingt deux)
83 quatre-vingt-et-trois (or quatre vingt trois)
84 quatre-vingt-et-quatre (or quatre vingt quatre)
85 quatre-vingt-et-cinq (or quatre vingt cinq)
86 quatre-vingt-et-six (or quatre vingt six)
87 quatre-vingt-et-sept (or quatre vingt sept)
88 quatre-vingt-et-huit (or quarte vingt huit)
89 quatre-vingt-et-neuf (or quatre vingt neuf)
For this grouping, you have the same first two words as the eighties (quatre-vingt), but add teens instead of single numbers.
For example, 90 literally means "four-twenty-ten" because it is twenty times four plus ten (20 x 4 + 10), and 91 means "four-twenty-eleven" (20 x 4 + 11).
See the direct translations next to each of these numbers below so you can understand what each word means.
90 quatre-vingt-dix (four twenty ten) kat-re van dees
91 quatre-vingt-onze (see above)
92 quatre-vingt-douze (four twenty twelve)
93 quatre-vingt-treize (four twenty thirteen)
94 quatre-vingt-quatorze (four twenty fourteen)
95 quatre-vingt-quinze (four twenty fifteen)
96 quatre-vingt-seize (four twenty sixteen)
97 quatre-vingt-dix-sept (f0ur twenty seventeen)
98 quatre-vingt-dix-huit (four twenty eighteen)
99 quatre-vingt-dix-neuf (four twenty nineteen)
French Numbers in the 100s
The triple digits have the same system as above, but they add the word cent to the front.
For numbers in the 100s, each French number will start with cent and add from there.
Below are a few examples of different combinations.
100 cent san
118 cent dix huit
122 cent vingt deux
124 cent vingt quatre
177 100 cent + 77 soixante dix sept = cent soixante dix sept
181 cent quatre vingt un
188 cent quatre vingt huit
194 cent quatre-vingt-quatorze
Numbers Above 200 in French
Each triple-digit number in French after the 100s will continue to use cent or cents. However, it will have a single digit before this word depending on what the number is.
For example, a number like 700 will start with sept (seven) and end with cents.
Based on this rule, the full name for 700 is sept cents.
Below, you can check out several examples of different types of triple digit numbers so that you can see all of the different ways in which they are written.
200 deux cents
217 deux cent dix sept
283 deux cent quatre vingt trois
295 deux cent quatre vingt quinze
298 deux cent quatre-vingt-dix-huit
300 trois cents
321 troi cent vingt et un
373 trois cent soixante treize
387 trois cent vingt sept
390 trois cent quatre vingt dix
399 trois cent quatre-vingt-dix-neuf
400 quatre cents
479 quatre cent soixante dix neuf
480 quatre cent quatre vingts
492 quatre cent quatre vingt douze
493 quatre cent quatre vingt treize
500 cinq cents
525 cinq cent vingt cinq
589 cinq cent quatre vingt neuf
597 cinq cent quatre vingt dix sept
685 six cent huitante cinq
688 six cent quatre vingt huit
French Numbers in the 1,000s
After you have mastered the three-digit numbers, moving on to the four-digit numbers will be a breeze!
Every number follows the same rules that you have learned above, but you will now add a new word, mille, into the mix.
As you can guess, this means one thousand. Below, you can explore a few examples of different combinations of four-digit numbers in French.
If you want to challenge yourself a bit more, try making your own combinations and using the lists above to create the French numbers.
1,080 mille quatre vingts
1,172 mille cent soixante douze
1,225 mille deux cent vingt cinq
1,991 mille neuf cent quatre vingt onze
3,071 trois mille soixante et onze
5,578 mille cinq cent soixante dix huit
6,000 six mille
Numbers in the Ten Thousands and Above
10,000 dix mille
100,000 cent mille
500,000 cinq cent mille
1,000,000 un million
1,000,000,000 un milliard
French Expressions for Counting
Now, let's take a look at some number-related vocabulary in French for various settings.
Multiplié par: multiply by
Divisé par: divide by
Pour cent: percent
Years in French
You can say years the exact same way that you would say the French four-digit numbers.
There are a few examples below.
For practice, think about the year you were born and some other important years and try to write them out.
1996: mille neuf cent quatre vingt seize
1899: mille huit cent huitante cinq
2005: deux mille cinq
First - premier/première
Second - deuxième
Third - troisième
Fourth - quatrième
Fifth - cinquième
Sixth - sixième
Seventh - septième
Eighth - huitième
Ninth - neuvième
Tenth - dixième
Summing Up French Numbers: How to Count in French from 1-100+
Congratulations, you have successfully mastered the art of counting in French from 1 to 100 and beyond. Gone are the days when French numbers seemed intimidating or confusing.
Armed with this newfound knowledge, you can confidently navigate any numerical conversation in the French language.
Remember to keep this comprehensive guide on hand as a quick reference whenever you need a reminder. With these charts and your determination, forgetting French numbers will be a thing of the past.
So go ahead, venture out into the world, and astound your friends with your impressive command of French numbers.
You're now equipped to embrace the beauty of this linguistic skill with confidence and grace. Bonne chance!


Invited paper “Non-Kochen–Specker Contextuality” by Mladen Pavičić, Entropy, 25(8), 1117 (2023), DOI: 10.3390/e25081117, has been selected as the cover paper of issue 8 of Entropy Volume 25 (2023) and the publication charges were waived.
The cover story reads as follows.
Let us consider a triangular hypergraph with three vertices and three hyperedges, each pairwise connecting two of the vertices. If we tried to assign 0 and 1 to vertices, so that just one vertex within each of the three hyperedges is assigned 1 (condition X), we would realize that this is not possible. The hypergraph exhibits a non-Kochen–Specker (KS) contextuality. Why “non-“? Because a KS hypergraph violates the same condition X, however in a space of dimension n ≥ 3 in which all of its hyperedges must contain n vertices. In an n-dim non-KS hypergraph at least one hyperedge has less than n vertices.
If we represented vertices by vectors in a hypergraph, n mutually orthogonal vectors in each hyperedge would be indispensable for an experimental implementation of the hypergraph, KS or not. But although all of them are needed for an implementation, we can choose some smaller set of the vertices when considering contextuality for an application, say, for quantum computation or quantum communication. If the hypergraph with chosen reduced number of vertices violated the aforementioned condition X, it would be a non-KS hypergraph.
How to generate non-KS hypergraphs? A previous method of obtaining them was of exponential complexity and their generation in dimensions higher than eight faced a computational barrier. Therefore, in this paper, we make use of dimensional upscaling which does not scale with dimension. This enables us to generate non-KS hypergraphs in well over 32-dimensional Hilbert spaces. In the paper we give explicit examples for all spaces up to 16-dim ones and show that the minimal number of hyperedges fluctuates between eight (odd dimensions) and nine (even dimensions) under the requirement that at least one the hyperedges contains n vertices, all of which share at least two hyperedges.


Please note that students will use the TI-Nspire CX handhelds developed by Texas Instruments in all of their math classes during the school year. If you want to buy a calculator for home use, the Crowley ISD Curriculum and Instruction Department recommends that you purchase the one used in your classroom. The TI-Nspire CX can be used on the eighth grade STAAR, Algebra 1 EOC, ACT, PSAT, SAT and AP tests.
If you purchase a TI-Nspire CX from a store or online, please have your students give the back of the box with the barcodes to their teacher. The school will have an opportunity to use these to receive free items from Texas Instruments for their classrooms.


Arithmetic Lesson PowerPoint Template
Arithmetic Lesson Presentation
Free PowerPoint template and Google Slides theme
Arithmetic is very useful in our lives. Teach your students the core arithmetic skills! Now use this creative template, which contains illustrations of books, cups, and science-related items. Use its maps, charts, timetables and tables to add your information.
With this template, you can add and subtract and multiply and divide easily in your classroom.
Features of this template
- 100% editable and easy to modify
- 27 different slides to impress your audience
- Contains easy-to-edit graphics such as tables, charts, diagrams and maps
- Includes 500+ icons for customizing your slides
- Designed to be used in Google Slides and Microsoft PowerPoint
- 16:9 widescreen format suitable for all types of screens
- Includes information about fonts, colors, and credits of the free resources used


We develop and analyse mathematical models to elucidate the fundamental mechanisms responsible of neuronal activity and its implications in computation and behaviour. Current projects involve the study of the mechanisms underlying oscillatory activity and its implications for the neuronal communication based on phase coherence; the development of mathematical techniques to address inverse problems of experimentally inaccessible features, such as synaptic conductances; the development and analysis of models of perceptual multistability.
Campus Diagonal Sud, Building H.
Av. Diagonal, 647
Perceptual multistability, Neuronal oscillations, Estimation of conductances, Slow-Fast systems


Gender inequality is a fact around the globe. According to the U.S. Department of Commerce, women occupy nearly half of all U.S. jobs, yet represent less than 25% of those in science, technology, engineering and math (STEM). The White House has framed the need for women in STEM careers as critical to the continuing success of the U.S. economy. According to the Department of Education, 31% of the degrees and certificates in STEM fields were earned by women in 2008-2009. While this represents an increase of approximately 6% since 2000, this is still troubling given that women represent over 50% of enrollment in bachelor’s (57.4%) and master’s (62.6%) degree-granting institutions.
To better understand the factors that could contribute to such imbalances, Gijsbert Stoet of the University of Leeds and David C. Geary of the University of Missouri looked at sex differences in math and reading achievement levels and their relationship with gender equality indicators. The resulting study, “Sex Differences in Mathematics and Reading Achievement Are Inversely Related: Within- and Across-Nation Assessment of 10 Years of PISA Data,” was published in PloS One in 2013. The researchers used data collected by the Programme for International Student Assessment (PISA), which included math and reading achievement data for nearly 1.5 million 15-year-olds in 75 countries.
The study’s findings include:
- Sex differences in math are inversely correlated with sex differences in reading, meaning that countries with smaller sex differences in math have larger sex differences in reading, and vice versa.
- The sex difference in math was negligible among the students at the bottom of the math achievement continuum, but the difference increased as performance levels rose. This difference ranged from 1.9 points favoring girls to 2.4 points favoring boys among boys and girls at the bottom 5% of achievers. At the high end of performance scores, the performance difference ranged from 19.3 points to 21.7 points, both favoring boys. The authors note that this large difference between boys’ and girls’ achievement in math has implications for the under-representation of women in STEM fields.
- Conversely, sex difference in reading is smaller at the high end of the performance continuum. The average sex difference in reading was three times larger than the sex difference in math. The average difference increased from 32 points in 2000 to 38.8 points in 2009. In 2009, the bottom 5% of boys scored 50 points lower than the bottom 5% of girls.
- Countries with higher living standards showed larger differences in math.
- Among all countries, as math and reading scores for both boys and girls go up, living standards and gender equality measures are more likely to be higher.
In considering possible approaches to closing the gender gap in STEM employment, the authors argue that increasing national prosperity is not enough. “The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics,” they state. “Interventions that focus on high-achieving girls in mathematics and on low-achieving boys in reading are likely to yield the strongest educational benefits.”
Tags: youth, higher education, technology


In sales, it’s important to understand how much effort you need to put in to achieve your income goals.
One way to do this is by understanding the conversion rates for each step in your sales process.
For example, if you know how many emails it takes to get an interview, how many interviews it takes to close a sale, and how much revenue each sale generates, you can start to predict your future income based on the amount of activity you put in.
Let's take a look at some hypothetical sales numbers to illustrate this concept:
- 20 emails convert to 1 interview, or 13 phone calls convert to 1 interview
- 5 interviews convert to 1 close
- 1 close generates $350 in revenue
Using these numbers, we can calculate how many emails, phone calls, interviews, and closes are needed to generate a specific amount of revenue. Here are some examples:
- For example, to earn $55,000 in revenue in a year, you would need to close 157 sales. To close 157 sales, you would need to conduct 785 interviews (157 x 5), which means you would need to have 15,700 emails sent out (785 x 20), or 10,201 phone calls (785 x 13).
- If you want to focus on increasing the number of phone calls you make, you could aim to make 30 calls a day. This would result in 2.3 interviews per day (30/13), and if you close 20% of those interviews, you would close 1 sale every 12 days (5 interviews / 20% = 1 sale, 12 days per sale). To earn $55,000 in revenue, you would need to close approximately 140 sales per year (55,000 / 350), which means you would need to make 690 phone calls per sale (140 sales x 5 interviews x 13 phone calls).
By understanding the conversion rates for each step in your sales process, you can start to set realistic goals for yourself and adjust your activity levels accordingly.
Whether you choose to focus on increasing the number of emails you send, the number of phone calls you make, or the number of interviews you conduct, it’s important to have a clear understanding of how each step contributes to your overall revenue goals.
Automate and simplify the whole calculation process with salesquotasetter.com
So you can measure your conversion rates and production. Know you averages easily with SQS. Set realistic targets that will earn you your commission you want!
Sign up now for a free trial and exceed your targets!


Conic optimization is a significant and thriving research area within the optimization community. Conic optimization is the general class of problems concerned with optimizing a linear function over the intersection of an affine space and a closed convex cone. One special case of great interest is the choice of the cone of positive semidefinite matrices for which the resulting optimization problem is called a semidefinite optimization problem.
Semidefinite optimization, or semidefinite programming (SDP), has been studied (under different names) since at least the 1940s. Its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve SDP problems (and more generally, to solve convex optimization problems with efficiently computable self-concordant barrier functions). Some of the earliest applications of SDP that followed this development were the solution of linear matrix inequalities in control theory, and the design of polynomial-time approximation schemes for hard combinatorial problems such as the maximum-cut problem.
The objective of this Handbook on Semidefinite, Conic and Polynomial Optimization is to provide the reader with a snapshot of the state of the art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. Our intention is to provide a compendium of the research activity that has taken place since the publication of the seminal Handbook mentioned above. It is our hope that this will motivate more researchers, especially doctoral students and young graduates, to become involved in these thrilling areas


A reader has requested that we give an explanation of cash on hand and profit. There seems to be some confusion about how the numbers work.
Cash on Hand is exactly what it sounds like – how much cash money is in the bank, right now?
If you’re looking at the balance in your checking account and add that to your savings account, that is “cash on hand.” Let’s assume that amount is $7500.
“Days cash on hand” = Cash on Hand / Daily Operating Expenses
Daily Operating Expenses = Annual Operating Expenses / 365
Let’s assume that it costs you $36,500 each year to run your household (Annual Operating Expense). If you divide that by the number of days in the year (365) you will get your “daily operating expense.”
$36,500 / 365 = $100 $100 is your daily operating expense.
Earlier, we said that you had $7,500 in your bank account (your “Cash on Hand”).
$7,500 / $100 = 75 You have 75 Days Cash on Hand. That means you have enough money to pay your bills for 75.
Profit is a different formula: Profit = Revenue – Expenses
Let’s assume you earn $42,000 each year (Revenue).
Your annual expenses are $36,5000 (Expenses).
$42,000 – $36,500 = $5,500 You had a “profit” of $5,500.
Notice that your profit of $5,500 is not equal to your cash on hand of $7,500.
Cash on Hand answers the question “how much cash do we have, right now?” That could on Jan. 1, Mar. 4, July 31, etc.
Profit answers the question “how much did we get to keep after we paid all the bills, during a certain time?”
The certain time could be a month, a quarter, or a year, “How much did we get to keep this year?”
For most people, the year starts on January 1 and ends December 31.
For Singing River, the year starts on October 1 and ends September 30.
When Singing River has a profit of $600,000 that answers the question “How much did SRHS keep after they paid the bills, from Oct 1, 2014 – Sept 30, 2015?”
According to the audit, as of Sept. 30, 2015, Singing River had $45 million cash on hand, which is approximately 51 days cash on hand.


SIGMA is an academic open-access journal which has been established for the dissemination of state-of-the-art knowledge in the field of mathematics and mathematics education. This journal published in Mathematics Education Department at Bondowoso University. It is published twice in a year (February and August). The SIGMA welcomes manuscripts resulted by researchers, scholars, teachers, and professionals from a research project in the scope of Pure Mathematics, Computing Mathematics, Statistics, Mathematics Learning, Evaluation and Assessment in Mathematics Learning, STEAM, Ethnomathematics, ICT in Mathematics Education, Design / Development Research in Mathematics Education and sciences. All submitted manuscripts will be initially reviewed by editors to ensure the quality of the published manuscripts in the journal. The manuscripts should be original, unpublished, and not in consideration for publication elsewhere at the time of submission to the SIGMA.


Gradient descent is an optimization algorithm that finds the local minimum of a function. The algorithm will take iterative proportional steps toward the negative gradient of the function at the current point. The algorithm usually starts with parameters (weights and bias) and improves them slowly as it tries to get a sense of the value of the cost function for weights that are similar to the current weights (by calculating the gradient). Then it moves in the direction which reduces the cost function by repeating this step thousands of times. The algorithm will continually minimize the cost function.
Next: Natural Language Processing


Experts in Statistics have advised more women to develop interest in Statistics and Data Science in order to harness their skills for better performance in their careers.
The call was made by various speakers at a South-East regional symposium to mark the 2020 International Year of Women in Statistics and Data Science at the Michael Okpara University of Agriculture, Umudike (MOUAU) in Abia.
It was organised by the Laboratory for Interdisciplinary Statistical Analysis (LISA) 2020 Network, MOUAU chapter, in collaboration with the International Statistical Institute (ISI).
Joy Nwabueze, a Professor of Statistics, said that it was important for more women to embrace statistics and data science.
She said that the more women there are in the area, the better for the realisation of the sustainable development goals.
Nwabueze, who is the first female Professor of Statistics in Nigeria, spoke on the topic: “Statistics and Good Governance: the role of Women in Statistics.”
She said that women in statistics and good governance would lead to greater economic stability and prevention of violence against women, amongst others.
She said that women in statistics are also good for development, adding that it would encourage the most use of the nation’s resources.
Nwabueze, who is the immediate past Vice-Chancellor (Administration) of MOAUA, said, “When women are into statistics, the family and society will be better.”
She said that good governance is participatory, consistent with rule of law, responsive, consensus-oriented, equitable and inclusive.
She further said that good governance is effective and efficient as well as accountable.
Also, Dr Hope Mbachu, a Statistics lecturer at the Imo State University (IMSU), encouraged more women to embrace statistics and data science, in order to be involved in social transformation.
According to her, social transformation is the main economic factor that moves countries forward.
Mbachu, who is the IMSU LISA Coordinator, spoke on “Strengthening Statistics and Data Science for Structural Development, the role of Female Statisticians.”
She said that the often neglected side of data science or statistics was the bane of using data erroneously.
Mbachu pointed out that where there was more gender equality, there would be more peace, among others.
“Women have made tremendous strides in Science, Technology, Engineering and Mathematics but there is still work to be done to achieve equality in what have been traditionally male-dominated disciplines,” she said.
The organiser and MOUAU LISA Coordinator, George Uchechukwu, said the programme was to commemorate the 200th anniversary of Florence Nightingale, who made landmark achievements in statistics and data science.
Uchechukwu, a lecturer in the Department of Statistics, MOAUA, advised female students to consider a career in statistics and data science, adding that opportunities abound in the field.
Earlier, the Vice-Chancellor of MOUAU, Prof. Francis Otunta, said the programme was important because there was a dearth of women in Mathematical Sciences.
Otunta, who was represented by Prof. Donatus Igbokwe, Dean, College of Physical and Applied Science, said the event would encourage more women to develop an interest in mathematical sciences, statistics and data science.
The News Agency of Nigeria (NAN) reports that the theme of the event is, “Connecting to build capacity to transform evidence into action and celebrate the International Year of Women in Statistics and Data Science.”


Share My Lesson offers free lesson plans, teacher resources and classroom activities created by dedicated educators. What we have below is a list of over 100 essential questions examples that we’ve created and collected over time. Note: All students following the Occupational Course of Study are also required to take English I, II, III, and IV, Math I, American History I and American History II, and Health and Physical Education. Common Core State Standards; Math Digital Textbook Content. The new K-8 Mathematics Standards were adopted June 1, 2017 for implementation 2018 - 2019. An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts—interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or designing a sewing pattern for the most efficient use of material. These curriculum maps are designed to address Common Core State Standards (CCSS) Mathematics and Literacy outcomes. The ACT College and Career Readiness Standards® are the backbone of ACT assessments. this is our classroom website. Visit archived Oklahoma's PK-12 academic standards. Bill McCallum's CCSS-M Learning Progressions pages within his blog, Tools for the Common Core. Cluster 2: Analyze, compare, create, and compose shapes. All standards identified on the blueprint are eligible to appear on a test form and should be taught during instruction. Congruence. Several states, once committed to adopting the standards, have opted to repeal them and move on to something else. Math in Practice is not another curriculum; it’s professional development in a book!. A circle is named by its center. These practices rest on important "processes and proficiencies" with long- standing importance in mathematics education. ELA-Literacy. Standards are a bold initiative. TEKS Review and Revision The State Board of Education (SBOE) has legislative authority to adopt the TEKS for each subject of the required curriculum. Medford Lakes School District Math Curriculum Guide – Algebra Survey Grade 8 Written by: Kathy O’Brien Text/Program: “Big Ideas” BOE Approved 8/19/15 EIGHTH GRADE MATHEMATICS - “Algebra Survey”. The standards emphasize depth over breadth, building upon key concepts as students advance. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set. Extended 1 st Grade Mathematics. To become familiar with the changes in the Extended Content Standards 4. Enduring Understandings and Essential Questions Mathematics K-12 Wallingford Public Schools Organization is based on the current State Frameworks in Mathematics. Fluency in Grades K-5. Alternate Assessment Consortium. The Alabama Learning Exchange includes multimedia, learning activities, lessons, and unit plans all “connected” by the Alabama Standards to promote deeper-learning competencies essential for success in college, careers, and our global society. Geometry in Construction is a team taught by both math and applied Technology teachers. Basic education in Washington state is defined by the Legislature (RCW 28A. Common Core is math, language arts and literacy standards fully adopted by 44 states and the District of Columbia. Mathematics: Focus by Grade Level. Loyalty policy – book your preferred writers without extra fees. The Nine Essential Skills are cross-disciplinary skills that students should be developing across grades K- 12. Geometry began to see elements of formal mathematical science emerging in Greek mathematics as early as the 6th century BC. Priority Standards are "a carefully selected subset of the total list of the grade-specific and course-specific standards within each content area that students must know and be able to do by the. would then be repeated with the three or four other Priority Standards assigned to these ELA and math units of study. grade 6 geometry measurement also available in docx and mobi. Answer C is the definition of opposite rays, which form a line. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. Understanding Summative Assessment Design. 150+ Essential Questions for Math. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada. The New York State Prekindergarten Learning Standards: A Resource for School Success, and the New York State Kindergarten Learning Standards: A Resource for School Success, are both now available for the 2019-20 school year. To learn about the process and how to get involved, take the Montana Content Standards 101 course on the Teacher Learning Hub (1 renewal unit). The Geometry Module effectively assists teachers in developing a deeper understanding of the underlying concepts that support the Texas Essential Knowledge and Skills (TEKS) in Geometry and helps teachers develop the pedagogical tools. In North Dakota, the content standards serve as a model. Standards-based curriculum has become the norm in education. In most cases, power standards are developed or selected at the school level by administrators and teachers. Each Element Card presents Essential Understanding(s), which define a range of skills based on a grade-specific Core Content Connector. (Gove, 1993) As you explore the resources and information provided by this LiveBinder the term curriculum refers to the essential standards and clarifying objectives of the standard course of study and any frameworks provided by the. 75 114th CONGRESS 1st Session H. All standards identified on the blueprint are eligible to appear on a test form and should be taught during instruction. GTPS Curriculum - Geometry 3 Weeks Topic: 6 - Inequalities in Geometry Objectives/CPI's/Standards Essential Questions/Enduring Understandings Materials/Assessment A-REI. Scribd is the world's largest social reading and publishing site. Created by experts, Khan Academy's library of trusted, standards-aligned practice and lessons covers math K-12 through early college, grammar, science, history, AP®, SAT®, and more. Extended K Mathematics. Browse or search thousands of free teacher resources for all grade levels and subjects. The material should be connected to real-world situations as often as possible, as suggested in the curriculum. A Correlation of Pearson Geometry, Common Core to the Common Core State Standards for Mathematics - High School PARRC Model Content Frameworks Mathematics Geometry ★ indicates modeling standards 1 SE = Student Edition TE = Teacher’s Edition Common Core State Standards for Mathematics - High School. The essential questions in this lesson are aligned to the Common Core State Standards for second grade mathematics. In Unit 6, seventh-grade students cover a range of topics from angle relationships to circles and polygons to solid figures. In April of 2014, the Indiana State Board of Education approved the adoption of new standards for Mathematics. House of Representatives 2013-10-31 text/xml EN Pursuant to Title 17 Section 105 of the United States Code, this file is not subject to copyright protection and is in the public domain. Note: All students following the Occupational Course of Study are also required to take English I, II, III, and IV, Math I, American History I and American History II, and Health and Physical Education. Delaware Content Standards English Language Arts Standards Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects. In the United States, the theory has influenced the geometry strand of the Standards published by the National Council of Teachers of Mathematics and the new proposed Common Core Standards. version of Singapore's most popular and proven math curriculum. Colorado Standards - Academic Standards The Colorado Academic Standards (CAS) are the expectations of what students need to know and be able to do at the end of each grade. High school geometry involves solving complicated proofs, and graphing and manipulating 3-D objects in 2-D space. The United States Academic Decathlon’s curriculum is an interdisciplinary curriculum in which a selected theme is integrated across six different subject areas: art, economics, literature, music, science, and social science. Geometry Statistics And Sequences. Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS) Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS) Amended Standard New Standard Deleted Standard. Geometry Quiz - Learning Connections Essential Skills Geometric Reasoning - solve tasks related to shapes and angles Problem Solving - work through a variety of. The standards are presented in a grade-by-grade sequence from pre-K through grade 8, and discrete strands address common high-school music classes, such as Ensembles and Music Composition/Theory. Geometry Module 1: Congruence, Proof, and Constructions. Introduction. Throughout the program the Standards for Mathematical Practice are seamlessly connected to the Common Core State Standards resulting in a program that maximizes both teacher. Moolenaar, Mr. These expectations are aligned to the Show-Me Standards, which define what all Missouri high school graduates should know and be able to do. Provide the Michigan Range of Complexity, which outlines how the skills associated with each target Essential Element (that will be measured as "state accessible") is to be. BrainPOP aligns all topics to the standards that matter to you, including CCSS, NGSS and U. The Standards for Mathematical Practice complement the content standards so that students increasingly engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and high school years. Common Core is math, language arts and literacy standards fully adopted by 44 states and the District of Columbia. 1(continued): Track geometry inspections, assessment and maintenance actions. For more detailed information about unpacking the content standards, unpacking a task, math routines and rituals, maintenance activities and more, please refer to the Grade Level Overview for fourth grade. These are all strategies that are emphasized by the Common Core State Standards, from elementary through secondary school. , we are truly in an exciting era of fulfilling and going beyond Richard Feynman's vision. RATHINDRA NATH has 3 jobs listed on their profile. The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. The California State Standards are a starting point for transforming the way we practice the art of teaching and for building stronger conversations among teachers, grade levels/departments, schools, districts, and states. Before now, students calculated area by. The Math Workgroup has made changes to the content emphasis documents based on what we have learned since 2010. The new standards have been the result of over two years of collaborative work to ensure New York State has the best learning standards for our students. What causes the geometric shapes of molecules? Electron pairs are as far apart as possible 3. The new standards provide teachers with frameworks that closely match the unique goals of their specialized classes. Yet, no one wants to teach to the test. The OGC has also produced the OGC Reference Architecture Profile Advisor, or RAP Advisor to help negotiate the ORM. Unwrapping the Standards: A Simple Way to Deconstruct Learning Outcomes. 114–107, Part I] IN THE HOUSE OF REPRESENTATIVES April 15, 2015 Mr. As announced in Superintendent’s Memo 043-19-This is a Word document. would then be repeated with the three or four other Priority Standards assigned to these ELA and math units of study. Geometry is the fourth math course in high school and will guide you through among other things points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles and area. Dynamic Learning Maps. The mathematics standards set a rigorous definition of college and career readiness by demanding that students develop a depth of understanding and ability to apply mathematics to real-life situations, as college students and employees regularly do. Understand how your team can use essential standards in your work. Tennessee Math Standards. The small one is that, for the rst time, special attention is paid to the need of a proof for the area formula for rectangles when the side lengths are fractions. Mathematical Process Standards Geometry G. Texas Essential Knowledge and Skills for Mathematics. BEST PRACTICES IN TEACHING MATHEMATICS Introduction Mathematics is a form of reasoning. Maryland calls these standards the Maryland College and Career-Ready Standards. A - Know number names and the count sequences. In my last post, I complained about the shrinkage of geometry, a decades-long trend in US math education. Note: All students following the Occupational Course of Study are also required to take English I, II, III, and IV, Math I, American History I and American History II, and Health and Physical Education. Let's look at the definition of a circle and its parts. Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS) Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS) Amended Standard New Standard Deleted Standard. This short video explains the difference between standards and curriculum. 113 HR 3080 EAS: Water Resources Development Act of 2013 U. Common Core Math Curriculum Kindergarten Diocese of Buffalo 2012 1 Math Common Core Curriculum - Kindergarten ESSENTIAL QUESTIONS DOMAINS AND CLUSTERS KINDERGARTEN SKILL VOCABULARY MATHEMATICAL PRACTICES & RESOURCES ASSESSMENT What are numbers? What is counting and how can it be used? Counting and Cardinality K. Create your own educational games, quizzes, class Web pages, surveys, and much more! Explore millions of activities and quizzes created by educators from around the world. ChrisN; We're haaving a version of a conversation that's been had by 2-3 other standards bodies, all of whom came to the decision to favor compatibility over enhancement. Grade 3, Adopted 2012. Each school district may set standards more rigorous than these state content standards, but no district shall use any standards less rigorous than those set forth in IDAPA 08. As required by state law, OSPI develops the state's learning standards (RCW 28A. Essential Assessment is a leading provider of a unique Australian Curriculum, Victorian Curriculum and NSW Syllabus numeracy and literacy assessment and curriculum model that delivers a whole school approach to formative and summative assessment for Australian schools. DONOTEDITTHISFILE!!!!! !!!!!$$$$$ !!!!!///// !!!"!&!&!+!+!S!T![!^!`!k!p!y! !!!"""'" !!!&& !!!'/'notfoundin"%s" !!!) !!!5" !!!9" !!!EOFinsymboltable !!!NOTICE. Overarching Essential Questions. 1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. It is still up to each local school district to adopt its own curriculum (how the standards are taught) to meet these standards. Schools and districts around the country are seeing continuous growth in student achievement using Eureka Math. For students first enrolled in Grade 9 in 2010-2011 or later, three of the Essential Skills are graduation requirements: Students prove that they have mastered these Essential Skills. Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. The topics covered include the definitions and properties of 2D and 3D shapes, the basic concepts and formulas of perimeter, area and volume, the Pick’s formula, the Cavalieri’s principles, the basic geometric transformations, the concepts of tessellations, the Euler’s polyhedral formula. (b) Introduction. Now to the topic of this post. The Essentials of High School Math was designed to help students learn the basics of mathematics that they are supposed to understand upon entering high school, as well as the fundamental lessons within Algebra, Geometry, and Statistics that students typically learn in ninth and tenth grade. Seventh grade state test scores were 62% last year and 70% proficient this year!" — Tammy S. Combined with unprecedented controllability of interactions, geometry, disorder strength, spectroscopy, and high resolution measurement of momentum distribution, etc. From the late 1970s forward, attempts have been made in the United States to provide a framework defining the basic essentials of mathematics that all students. Welcome to Bright Ideas, the e-newsletter of Illuminations. As required by state law, OSPI develops the state's learning standards (RCW 28A. Provide the Michigan Range of Complexity, which outlines how the skills associated with each target Essential Element (that will be measured as "state accessible") is to be. Click on each section of the graphic below to explore more. essential questions. Unit Essential Questions. Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011. This document is designed to help North Carolina educators teach the 5th Grade Mathematics Standard Course of Study. B | Understand and apply the Pythagorean Theorem. The frameworks that follow are the result of this work. Focusing on critical and analytical. These practices rest on important "processes and proficiencies" with long- standing importance in mathematics education. Each lesson covers a different standard, gives the objective, new vocabulary words that were introduced, and a video that explains the homework sheet. instruction. GTPS Curriculum – Geometry 3 Weeks Topic: 6 - Inequalities in Geometry Objectives/CPI’s/Standards Essential Questions/Enduring Understandings Materials/Assessment A-REI. NCTE/IRA Standards for the English Language Arts. ] textbooks are often weak, the presentation becomes more mechanical than is ideal. The Queensland Curriculum and Assessment Authority is a statutory body of the Queensland Government. Lucas, Mrs. First Grade Math: Geometry Standards. The New York State Prekindergarten Learning Standards also aligned with the existing New York State K-12 learning standards in science, social studies, and the arts. when the CCSS-M authors wrote the standards and sequenced them into grades as they did, be sure to visit Dr. 1 Count, read, and write whole numbers to 100. the standards and, as needed, provided statements to help teachers comprehend the full intent of each standard. So off you go!. 102, page 11. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set. The Go Math Program is designed to go along with the Common Core Standards. The National Council of Teachers of Mathematics' view of how school geometry should look. The curriculum introduces geometric topics, skills, and concepts. Principles and Standards for School Mathematics outlines the essential components of a high-quality school mathematics program. php(143) : runtime-created function(1) : eval()'d code(156) : runtime-created function(1. The Common Core State Standards for English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects (“the Standards”) are the culmination of an extended, broad-based effort to fulfill the charge issued by the states to create the next generation of K–12 standards in order to help. , having four sides), and that the shared attributes can. Resources on Wisconsin Standards for Mathematics. Extended 3 rd Grade Mathematics. com FREE SHIPPING on qualified orders. The seventh-grade Geometry standards are categorized as additional standards, however, there are several opportunities throughout the unit where students are engaged in the major work of the grade. 7 1 Common Core Math Curriculum Grade 7 ESSENTIAL QUESTIONS DOMAINS AND CLUSTERS GRADE 7 SKILL VOCABULARY MATHEMATICAL PRACTICES ASSESSMENT What are the properties of operations? How do you translate real-world problems to algebraic expressions? What is the difference between a rational and irrational number?. But, teaching the addition facts doesn’t have to be like this. The Helpful Hints section teaches the next concept. Essential Understanding Studentswill be expected to be able. Chegg's step-by-step geometry guided textbook solutions will help you learn and understand how to solve geometry textbook problems and be better prepared for class. essential questions. HID Global’s Lumidigm multispectral imaging fingerprint technology has been certified compliant with the ISO/IEC 30107-3 Presentation Attack Detection (PAD) standard, after receiving a perfect score in certification testing by independent lab iBeta Quality Assurance. IB Union Calendar No. Welcome to the Kansas State Department of Education website devoted to the Kansas Curricular Standards. Math in Practice is a standard-based, professional learning resource from Sue O'Connell and colleagues. At each grade, students are expected to not only develop an understanding of content standards, but also develop key behaviors outlined in. March 7, 2012. Extended K Mathematics. Common Core Georgia Performance Standards High School Mathematics CCGPS Analytic Geometry ‐ At a Glance Common Core Georgia Performance Standards: Curriculum Map 1st Semester 2nd Semester Unit 1 Unit 2 Unit 3 Unit 4a Unit 4b Unit 5 Unit 6 Unit 7 Similarity, Congruence, and Proof. B | Understand and apply the Pythagorean Theorem. High School Geometry Common Core Math Tests:. The Common Core State Standards for language arts get students reading deeply and connecting with what they have read. The heart of the module is the study of transformations and the role transformations play in defining congruence. To do so would strip. All worksheets created. Listed below are the sub-categories or worksheets in Geometry Worksheets. Performance-level descriptors describe what a typical student at each level should be able to demonstrate based on his/her command of grade-level standards. The Tennessee State Math Standards were reviewed and developed by Tennessee teachers for Tennessee schools. The next Smartgeometry Conference (sg2016) will take place at the Chalmers University of Technology in Gothenburg, Sweden, April 4-9, 2016. TABLE OF CONTENTS Introduction. Visual art is a natural place for students to apply their knowledge and understanding of geometric concepts. The standards are helping educators and education leaders worldwide re-engineer schools and classrooms for digital age. Mathematics Standards Download the standards Print this page For more than a decade, research studies of mathematics education in high-performing countries have concluded that mathematics education in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. TCSS GSE Geometry Unit 2 Curriculum Map TCSS 7/30/2016 2. We demonstrate. Assessment: Standards-aligned assessment, a routine part of ongoing classroom activity, should enhance students' learning and inform instructional decisions. of Public Instruction Exceptional Children Division 1 Objectives 1. Family Math Night Math Standards In Action. Imagine Math (IM) is an online, supplemental math instruction and tutoring program that will help raise student achievement in Idaho by providing students with focused instruction, rigorous math problems, access to live certified teachers, and a motivation program with rewards for working on math problems. 4 Reading Standards and Interpreting their Codes in High School Courses. For a variety of kindergarten vocabulary words to help get a handle on mathematics, look no further than VocabularySpellingCity! Our Kindergarten math terms will help your students get the upper hand on this tough to learn subject by helping them understand what the different terminology means. Common Core Standards: 4. , Assistant Principal from Pullman, WA. The study of Geometry offers students the opportunity to develop skill in reasoning and formal proof. ; Fichtl, G. They are organized by conceptual categories or themes: Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Data. We have done math centers every day this week and most of last week. The standards serve as goals for teaching and learning. The Texas Performance Standards Project (TPSP) comprises a set of performance standards, curricula, and assessments for differentiating instruction and deepening academic learning. Designed and manufactured in the U. 2 sum 1 | Relation and function with two set of values | ordered pair. The Curriculum Division mathematics team provides direction and leadership to the mathematics programs, Kindergarten through grade 12. Welcome to Bright Ideas, the e-newsletter of Illuminations. The Chinese automaker – and Volvo owners – revealed not. 1 Count, read, and write whole numbers to 100. Gwinnett’s curriculum for grades K–12 is called the Academic Knowledge and Skills (AKS) and is aligned to the state-adopted Georgia Standards of Excellence in Language Arts (K-12), Mathematics (K-12), and literacy standards for Science, Social Studies, and Technical Education for middle and high school students. 0 Construct using straight edge and compass. Before now, students calculated area by. Essential questions organically inspire the kinds of narrative, informational, and persuasive writing required by the Common Core. Extended K Mathematics. These standards are developed by each state. gov/femp/ Introduction Incorporating energy efficiency, renewable energy, and sustainable green design features into all Federal. Throughout the program the Standards for Mathematical Practice are seamlessly connected to the Common Core State Standards resulting in a program that maximizes both teacher. Geometry made simple and relevant This series is going Out of Print. NCTE/IRA Standards for the English Language Arts. Overarching Essential Questions. The Essentials of High School Math was designed to help students learn the basics of mathematics that they are supposed to understand upon entering high school, as well as the fundamental lessons within Algebra, Geometry, and Statistics that students typically learn in ninth and tenth grade. There are so many great lesson plans and resources out there for arts integration in geometry. Academic Standards + Grade Level Expectations. 373X100001 from the U. McCallum frequently responds within. 1 Describe objects in the environment using names of shapes, and describe the relative positions of objects using positional terms. This is a first grade blog designed to help my class with our Go Math Program. Please click the links below to see suggested replacement series: AGS Geometry Power Basics Geometry Through a clear and thorough presentation, this comprehensive program fosters learning and success for students of all ability levels with extensive skills practice, real-life. Given a number from 1 to 24, output the kissing number to the best of current knowledge (some numbers will have more than one acceptable output). During this period, the content of geometry and its internal diversity increased almost beyond recognition; the axiomatic method, vaunted since antiquity by the admirers of. The initial draft of the Dynamic Learning Maps Essential Elements (then called the Common Core Essential Elements) was released in the spring of 2012. No hidden charges – a fair policy is essential for our relation with the customers. In this article, you’ll learn everything you need to know to teach your child the addition facts—without killing your kid’s love of math or wanting to poke your eyeballs out in the process. For students first enrolled in Grade 9 in 2010-2011 or later, three of the Essential Skills are graduation requirements: Students prove that they have mastered these Essential Skills. Hultgren, Mr. Jasmine's class wrote stories about various animals that focused on the setting of their habitats, and wrote informational texts using summary, description, and comparison. Math Connects is correlated to the Common Core State Standards! Click the CCSS logo to check out the new CCSS lessons and homework practice pages. A closed-form equation is derived for root mean square (rms) value of velocity change (gust rise) that occurs over the swept area of wind turbine rotor systems and an equation for rms value of velocity change that occurs at a single point in space. The heart of the module is the study of transformations and the role transformations play in defining congruence. Geometry is an important part of mathematics, one that deals with shapes and spatial relationships. Welding Procedure Specifications (WPS) This document details the practical application of the Procedure Qualification Record (PQR). Math Progressions Prior to the development of the Common Core State Standards in Mathematics, a series of documents were produced by writers of the Common Core that described a specific topic or concept across a number of grade bands. Find the right K-12 lesson plans - for free. First Grade Standards, First Grade Math Standards, First Grade Math, First Grade Skills, Math Standards First Grade, Geometry Standards, Shape Standards. Reading: Literature Standards; Reading: Informational Text Standards. Sep 25, 2019- Grade 5 materials and resources, lessons, printables, worksheets, projects, and games for Science, especially the NC Essential Standards. state standards. The material should be connected to real-world situations as often as possible, as suggested in the curriculum. 12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc. Personally, think it is a worthwhile subject of study, but I don't think that there is much demand for it in today's design environment. Enduring Understandings Essential Questions. Mathematics Course Updates for 2018–2019 • Differential Equations. Read grade 6 geometry measurement online, read in mobile or Kindle. This is a first grade blog designed to help my class with our Go Math Program. NOTICE: Comments, as submitted, shall be filed with the West Virginia Secretary of State's Office and open for public inspection and copying for a period of not less than five years. And, in most districts, standardized tests are the way understanding is measured. are repeated. Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. 1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. Internet: http://www. Thinking mathematically consists of thinking in a logical manner, formulating and testing conjectures, making sense of things, and forming and justifying judgments, inferences, and conclusions. The competency committee members looked at existing competencies within and outside of our state, Oklahoma high school and college course syllabi, vertical alignment documents, our Oklahoma Academic Standards for Mathematics, and the NCTM Essential Standards for High School Mathematics to determine which essential skills should be included in. The topics covered include the definitions and properties of 2D and 3D shapes, the basic concepts and formulas of perimeter, area and volume, the Pick’s formula, the Cavalieri’s principles, the basic geometric transformations, the concepts of tessellations, the Euler’s polyhedral formula. It provides students with the mathematical knowledge, skills and understanding to solve problems in real contexts for a range of workplace, personal, further learning and community settings. “Unwrap” the Standards Definition of “unwrapping”: The analysis of standards and. The first of. These standards are designed to complement other national, state, and local standards and contribute to ongoing discussions about English language arts. Review the geometry topics youve been learning in class with this convenient and self-paced high school geometry course. Math Curriculum Kindergarten 3. Domain: OPERATIONS AND ALGEBRAIC THINKING Cluster 1: Use the four operations with whole numbers to solve problems. The aim was to create a set of common learning expectations for Mathematics and for English Language Arts/Literacy in subjects including literature, history. Standards for Mathematical. Geometry is an important part of mathematics, one that deals with shapes and spatial relationships. Overarching Essential Questions. A super beneficial offer for every customer. TPSP enhances gifted/talented (G/T) programs from kindergarten through high school. High School: Geometry » Introduction Print this page. Essential Standards" Essential Standards; Technology" Chromebooks; Essential Standards. , having four sides), and that the shared attributes can. In addition to the requirement that students meet those content standards, students must also (to the extent practicable) develop and demonstrate skills (Fig. To what extent do we make connections to build relationships between algebra, arithmetic, geometry, measurement, discrete mathematics, probability and statistics? Representing mathematical ideas involves using a variety of representations such as graphs, numbers, algebra, words, and physical models to convey practical situations. Illuminations Navigation Guide. Clear statements about what students must know and be able to do are essential to ensure students are given the opportunity to succeed. The standards serve as goals for teaching and learning. essential questions. Everything At One Click Sunday, December 5, 2010. Common Core Math Curriculum Kindergarten Diocese of Buffalo 2012 1 Math Common Core Curriculum - Kindergarten ESSENTIAL QUESTIONS DOMAINS AND CLUSTERS KINDERGARTEN SKILL VOCABULARY MATHEMATICAL PRACTICES & RESOURCES ASSESSMENT What are numbers? What is counting and how can it be used? Counting and Cardinality K. In the nineteenth century, geometry, like most academic disciplines, went through a period of growth verging on cataclysm. Personally, think it is a worthwhile subject of study, but I don't think that there is much demand for it in today's design environment. Grade 8 Math Revised 07/2008 5 Topic: Geometry/2-D Angles Essential Questions: How is geometry used in life? Performance Indicators Guided Questions Essential Knowledge and Skills Classroom Ideas (Instructional Strategies) Assessment Idea s (evidence of understanding) 8. Common Core and Essential Standards Extended Content Standards Claire Greer Dept. Pilot Eureka math. The NCTM published the process standards in Principles and Standards for School Mathematics. Los Angeles Unified School District Office of Curriculum Instruction and School Support 2014-2015 Common Core Geometry Curriculum Map LAUSD Secondary Mathematics Overview of the Curriculum Map – Geometry June 2, 2014 Draft Page 2 Mathematical literacy is a critical part of the instructional process, which is addressed in:. This provides a rich yet balanced curriculum- attention to numeration and computation without neglecting geometry, data, and algebraic thinking. Geometry is an important part of mathematics, one that deals with shapes and spatial relationships. No hidden charges – a fair policy is essential for our relation with the customers. This High School Geometry Web Guide can be a valuable resource for geometry help and final exam preparation for students, a source of geometry lesson plans for teachers and a geometry refresher for parents. Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS) Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS) Amended Standard New Standard Deleted Standard. The standards emphasize depth over breadth, building upon key concepts as students advance. Standards for Mathematical Practice Common Core State Standards for Mathematics To emphasize the Mathematical Practices, the CCSS gives them their own distinct section, but they are not to be thought of as a separate skill set to be handled in special lessons or supplements. All worksheets created. essential standards chart grade 6 math - Free download as Word Doc (. 1) essential for success in professional life. Math was essential to everything from the first wireless radio transmissions to the prediction and discovery of the Higgs boson and the successful landing of rovers on Mars. The Geometry course outlined in this document begins with developing the tools of geometry, including transformations, proof, and constructions. Browse or search thousands of free teacher resources for all grade levels and subjects. 7 Integrate visual information (e. Knowledge of geometry is not essential as the outputs. Assessment: Standards-aligned assessment, a routine part of ongoing classroom activity, should enhance students' learning and inform instructional decisions. INTRODUCTION. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. content in the Common Core State Standards to academic expectations for students with the most significant cognitive disabilities. Welcome to Achieve the Core. Extended K Mathematics. (1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. High School Office; High School Principal's Page; 2019-2020 Course Registration Handbook; Counselor's Corner; High School Daily Schedule; Lunch Menus; 2019-2020 School Supply Lists. BIM handbook: A guide to building information modeling for owners, managers, designers, engineers and contractors. To what extent do we make connections to build relationships between algebra, arithmetic, geometry, measurement, discrete mathematics, probability and statistics? Representing mathematical ideas involves using a variety of representations such as graphs, numbers, algebra, words, and physical models to convey practical situations.


YOUTH MENTAL MATH
Studying mathematics is not limited to studying quantities and graphs. Mathematics allows children to develop the ability to think using mathematical logic. Learning the mental math is like mental gymnastics for a child’s intellectual development, it is also a strong way in developing a child’s ingenuity and dexterity. Because the mental math requires learners to simultaneously use their heads and hands to compute, the process effectively stimulates cerebral development, exposes intellectual potential, and grants continuous growth for the learner.
In this course, students will learn how to calculate mathematical problems using the abacus. The standard abacus can be used to perform addition, subtraction, division, and multiplication. The abacus can be used to calculate with great speed.
Course ID: T7100
No. of Classes: 10
Instructor: Lucy Ao


I decided to create the Toronto Raptors logo using graphs on Desmos. I decided to create this logo because it involved circle equations, quadratic, square root, linear, and trig functions. I used circle equations to create the outside of the ball, as well as the lower vertical curves on the basketball. I changed the radius and the multiplier on the x/y variables to match the shape. I used quadratic equations to create the horizontal and vertical-middle basketball curves because they fit the small curve shape. I compressed, vertically and horizontally translated, and reflected the graph. I used square root functions to create the vertical-upper basketball curves because it fit the medium curves. I horizontally and vertically translated the graph. I used a trig function for one of the horizontal-middle curves because the sin function matched the light curve of the ball. I also needed a new equation. Finally, I used linear equations for the claw marks on the ball. The claws required a series of straight lines, hence why I used a linear equation. The major challenge I encountered was completing the claw marks. There were so many of them and it took me a long time to complete them. Copying and pasting equations helped me speed it up. I asked other students for input on how to manipulate my graph to make it match. My strategy at the end was to use the sliders to find the values and input them into the variables. I didn’t use this strategy at the beginning, so I had to change all my equations and delete the sliders at the end. Through this project I learned how transform functions with translations, expressions/compressions, and reflections through variables in equations.


This article continues from the previous article, by continuing the trend into even larger numbers. These are Numbers that are rarely mentioned outside of tables of large figures cited in physics and astronomy ...
Next up ...
At this point it's getting difficult to keep track of all of those zeroes. One sextillion is rarely heard of, and not well known, but it is officially recognized and the legitimate continuation after quintillion. One Sextillion is 1 followed by 21 zeroes ( 7 groups of 3 ).
The earth has a mass of about 5.98 Sextillion metric tons ( 1 Metric Ton = 1000 kilograms ).
There are about 6 sextillion cups of water in all the oceans of the world
The volume of the earth is about 1.085 Sextillion cubic meters.
The distance between one end of the universe and the other may be about 87.9 sextillion miles !
Now another order of a thousand ...
One Septillion is 1 followed by 24 zeroes ( 8 groups of 3 zeroes ). A Septillion is a Trillion Trillions !
One liter of water contains about 33.4 Septillion water molecules.
The earth has a mass of about 5.98 Septillion kilograms.
One Octillion is 1 followed by 27 zeroes ( 9 groups of 3 zeroes ) . An octillion is a billion billion billions !! It's almost impossible to even comprehend that.
The earth has a mass of about 5.98 Octillion grams.
The mass of the sun is about 1.989 Octillion metric tons.
The volume of the sun is about 1.412 Octillion cubic meters
One Nonillion is 1 followed by 30 zeroes ( 10 groups of 3 zeroes ). A nonillion is a quadrillion quadrillions !? Or a million trillion trillions.
The mass of the sun is about 1.989 nonillion ( 1.989x10^30 ) kg
One Decillion is 1 followed by 33 zeroes ( 11 groups of 3 zeroes ).
The Area of the Milky Way galaxy is approximately 702 Decillion square kilometers.
The mass of the sun is about 1.989 decillion ( 1.989x10^33 ) grams
One Undecillion is 1 followed by 36 zeroes ( 12 groups of 3 zeroes ).
The volume of the M Supergiant Star , Betelguese , is roughly 1.21 undecillion cubic meters.
One Duodecillion is 1 followed by 39 zeroes ( 13 groups of 3 zeroes ).
The great lakes contain roughly 52.92 duodecillion water molecules !!
One tredecillion is 1 followed by 42 zeroes ( 14 groups of 3 zeroes ).
There are about 200 Tredecillion atoms contained in the entire atmosphere of earth
There is about 100 tredecillion grams of matter contained in the grand total of all the stars in the milky way galaxy.
One quattuordecillion is 1 followed by 45 zeroes ( 15 groups of 3 zeroes ), and yes that is the official name. quattuor means "four" in latin, and deci means "ten".
There are about 41.75 quattuordecillion water molecules in all the water on the earth.
One quindecillion is 1 followed by 48 zeroes ( 16 groups of 3 zeroes ). A quindecillion is equal to a trillion trillion trillion trillions !
The earth is composed of about 89 quindecillion molecules
One Sexdecillion is 1 followed by 51 zeroes ( 17 groups of 3 zeroes ).
The volume of the milky way galaxy is about a sexdecillion cubic miles
One Septendecillion is 1 followed by 54 zeroes ( 18 groups of 3 zeroes ).
The Volume of the Pleiades star cluster ( a near by star cluster within the milky way galaxy ) is roughly 226 Septendecillion cubic centimeters
One Octodecillion is 1 followed by 57 zeroes ( 19 groups of 3 zeroes ).
The Pleiades star cluster may contain roughly 800 Octodecillion hydrogen atoms
One Novemdecillion is 1 followed by 60 zeroes ( 20 groups of 3 zeroes ).
The Volume of the milky way galaxy is about 147 Novemdecillion cubic feet.
One Vigintillion is 1 followed by 63 zeroes ( 21 groups of 3 zeroes ). Currently it is the largest "official illion" that is part of a continuous nomenclature starting from million , billion , trillion , etc.
The volume of the sphere approximating the Virgo Super Cluster ( The super cluster in which we reside ) is roughly 3.54 Vigintillion cubic kilometers
ONE THOUSAND VIGINTILLION
A Thousand Vigintillion does not have a proper number name, there is no "illion name" for it. Scientists are perfectly comfortable using "scientific notation" and calling it simply "ten to the sixty sixth". The most common proposal for this number is naturally enough "unvigintillion", based on the trend established with decillion, undecillion, duodecillion, etc.
There are about a thousand vigintillion atoms in our galaxy
ONE MILLION VIGINTILLION
One million vigintillion is also known by number ethusiasts as "duovigintillion".
Note that by the time we reach numbers this big, it becomes very difficult to think of any example at all, not because numbers this big don't have physical representers, but simply because it is difficult to find an example that falls exactly in this range.
The Volume of the observable universe may be roughly a million vigintillion cubic miles
The Virgo Super cluster may contain close to 200 million vigintillion hydrogen atoms in it's 200 trillion stars
ONE BILLION VIGINTILLION
One Billion vigintillion, better known simply as "trevigintillion".
The volume of the virgo super cluster is roughly 3.54 billion vigintillion cubic meters.
The volume of the great wall Super structure ( a giant "filament" composed of galaxy clusters ) is roughly 1.9 billion vigintillion cubic meters
ONE TRILLION VIGINTILLION
One Trillion vigintillion, also called "quattuorvigintillion".
Unfortunately I was not able to come up with an example for this tremendous number, although there must certainly be a trillion vigintillion of something because this number is smaller than the lower bound for the number of sub-atomic particles in the observable universe. Let's just say that there is about a trillion vigintillion sub-atomic particles in 1/1000 of the volume of the observable universe.
ONE QUADRILLION VIGINTILLION
One Quadrillion vigintillion , also called "quinvigintillion".
It is estimated that the observable universe may contain roughly a quadrillion vigintillion sub-atomic particles
ONE QUINTILLION VIGINTILLION
One Quintillion vigintillion, also called "sexvigintillion".
The volume of the universe is roughly a quintillion vigintillion cubic feet
ONE SEXTILLION VIGINTILLION
One Sextillion vigintillion, also called "septenvigintillion".
The volume of the universe is roughly a sextillion vigintillion cubic inches
ONE SEPTILLION VIGINTILLION
One Septillion vigintillion, also called "octovigintillion".
The Volume of the universe is about 47 septillion vigintillion cubic millimeters.
ONE OCTILLION VIGINTILLION
Also called "novemvigintillion".
ONE NONILLION VIGINTILLION
Also called "trigintillion", from the latin word "triginta" for 30.
ONE DECILLION VIGINTILLION
Because of the tremendous scale of these numbers, it is no longer practical to make jumps of a 1000 fold. Instead I will now be making jumps of a billion fold ! Because of this certain "illions" here will have no entries.
One decillion vigintillion is also called "untrigintillion".
The Volume of the universe is 47 decillion vigintillion cubic micrometers.
A micrometer = 10^-6 meters. Microbes can be measured in micrometers.
ONE UNDECILLION VIGINTILLION
Also called "duotrigintillion".
ONE DUODECILLION VIGINTILLION
Also called "tretrigintillion".
ONE TREDECILLION VIGINTILLION
One tredecillion vigintillion is also called "quattuortrigintillion".
The volume of the universe is 47 tredecillion vigintillion cubic nanometers.
A nanometer = 10^-9 meters.
Note: Recall that a Googol = 10^100 . This means that the volume of the universe is
4,700,000 googol cubic nanometers. The Googol is often regarded as impractically large, an not representative of anything in reality. However when we consider the entirety of the known universe divided by the some of the smallest known units of space, we easily exceed the googol. This proves that numbers as big as a "googol" are not as impratical and meaningless as once thought.
ONE QUATTUORDECILLION VIGINTILLION
Also called "quintrigintillion".
ONE QUINDECILLION VIGINTILLION
Also called "sextrigintillion".
ONE SEXDECILLION VIGINTILLION
One sexdecillion vigintillion is also called "septentrigintillion".
The volume of the universe is 47 sexdecillion vigintillion cubic picometers.
A picometer = 10^-12 meters.
ONE SEPTENDECILLION VIGINTILLION
Also called "octotrigintillion".
ONE OCTODECILLION VIGINTILLION
Also called "novemtrigintillion".
ONE NOVEMDECILLION VIGINTILLION
Also called "quadragintillion" from the latin word "quadraginta" for 40.
The volume of the universe is 47 novemdecillion vigintillion cubic femtometers.
A femtometer = 10^-15 meters. It is said that the diameter of protons and neutrons is about 1 femtometer, and that this is also the range of the strong nuclear force.
ONE VIGINTILLION VIGINTILLION
Also called "unquadragintillion".
ONE THOUSAND VIGINTILLION VIGINTILLION
Also called "duoquadragintillion".
ONE MILLION VIGINTILLION VIGINTILLION
Also called "trequadragintillion".
The volume of the universe is 47 million vigintillion vigintillion cubic attometers.
An attometer = 10^-18 meters. It is said that the diameter of electrons and quarks is about 1 attometer.
ONE BILLION VIGINTILLION VIGINTILLION
Also called "quattuorquadragintillion".
ONE TRILLION VIGINTILLION VIGINTILLION
Also called "quinquadragintillion".
ONE QUADRILLION VIGINTILLION VIGINTILLION
Also called "sexquadragintillion".
The volume of the universe is 47 quadrillion vigintillion vigintillion cubic zeptometers.
A zepto meter = 10^-21 meters.
ONE QUINTILLION VIGINTILLION VIGINTILLION
Also called "septenquadragintillion".
ONE SEXTILLION VIGINTILLION VIGINTILLION
Also called "octoquadragintillion".
ONE SEPTILLION VIGINTILLION VIGINTILLION
Also called "novemquadragintillion".
The volume of the universe is 47 septillion vigintillion vigintillion cubic yoctometers.
A yoctometer = 10^-24 meters.
ONE OCTILLION VIGINTILLION VIGINTILLION
Also called "quinquagintillion" from the latin word "quinquaginta" meaning 50.
ONE NONILLION VIGINTILLION VIGINTILLION
Also called "unquinquagintillion".
ONE DECILLION VIGINTILLION VIGINTILLION
Also called "duoquinquagintillion".
The volume of the universe is 47 decillion vigintillion vigintillion cubic milli-yoctometers.
A milli-yoctometer = 10^-27 meters. Normally one is not allowed to combine prefixes, but in this case there is no prefix for 10^-27. We will learn more about this in the next chapter when we discuss SI prefixes.
ONE UNDECILLION VIGINTILLION VIGINTILLION
Also called "trequinquagintillion".
ONE DUODECILLION VIGINTILLION VIGINTILLION
Also called "quattuorquinquagintillion".
ONE TREDECILLION VIGINTILLION VIGINTILLION
Also called "quinquinquagintillion".
The volume of the universe is 47 tredecillion vigintillion vigintillion cubic micro-yoctometers.
A micro-yoctometer = 10^-30 meters.
ONE QUATTUORDECILLION VIGINTILLION VIGINTILLION
Also called "sexquinquagintillion".
ONE QUINDECILLION VIGINTILLION VIGINTILLION
Also called "septenquinquagintillion".
ONE SEXDECILLION VIGINTILLION VIGINTILLION
Also called "octoquinquagintillion".
The volume of the universe is 47 sexdecillion vigintillion vigintillion cubic nano-yoctometers.
A nano-yoctometer = 10^-33 meters.
ONE SEPTENDECILLION VIGINTILLION VIGINTILLION
Also called "novemquinquagintillion".
ONE OCTODECILLION VIGINTILLION VIGINTILLION
Also called "sexagintillion" from the latin word "sexaginta" meaning 60.
There is a theoretical "smallest unit of distance" that arrises in modern physics. It is the result of combining quantum mechanics with general relativity. In general relativity deals with the large scale features of our universe, while quantum mechanics deals with the small scale features.
In general relativity, gravity is reinterpreted as a force which distorts the fabric of space-time, and by doing so, effects the motion of neighboring objects. In otherwords, the theory says that the presense of matter distorts the local space-time.
In Quantum mechanics, what we can't observe is ultimately unknowable. It postulates that at the smallest scale the universe is random and chaotic, and is only governed by laws of statistics. As a by-product of this, it is said that on small scales, "virtual particle pairs" can spontanteously pop in and out of existence. Because these virtual particles are created and destroyed so rapidly, it is argued, that the conversation law of mass-energy is not broken. Another even weirder consequence of the theory is that as the scale gets smaller and smaller, more energy will pop in and out of existence in shorter time frames.
When we combine the 2 theories there is an interesting result. As we go down into smaller and smaller scales, eventually we encounter a scale where highly massive virtual pairs are created. Because of the huge amount of mass, general relativity says there will be a very huge local distruption in the space-time fabric. Eventually these distortions become so severe that the equations literally explode. This "bubbly space-time" is sometimes refered to as "quantum foam".
The result is that the continuity and consistency of space and time ceases to be meaningful. It is said that concepts such as "here" or "there", "past" and "future", get scrambled, so that there is no concept of sequence.
It is therefore impossible to measure distances smaller than this threshold. Hence, it becomes meaningful to talk of a "smallest possible distance that can be meaningfully measured". This minimum distance is called the "Planck Length", and it is approximately 10^-35 meters. So Now what if we take the entirety of the known universe and divide it by the smallest possible spatial unit ? ...
In this case we can say that the volume of the universe is 47 octodecillion vigintillion vigintillion cubic Plank lengths, that's 4.7 x 10^184 Pl^3 .
Note that this volume is computed by treating the universe as if it were the hyper-surface of a 4-dimensional sphere ( sometimes called the "glome" among the polychorists ). One can think of this "glome" as starting out as an infintesimal point at the big bang, and then expanding like a 4 dimensional balloon 4-space. In other words, this volume is only the volume of the universe 'now'. At an earlier time the volume would have been smaller, and in the far future it may be much larger still ! And notice the exponent, 184. Most people think numbers these large have no physical meaning, but what these estimates show is that they may very well represent tangable and measurable things !!
So that's it right ? We have reached the end of physical numbers ... not quite. Assuming the universe will continue to exist and expand the volume will increase with time. Cosmologists usually say the big bang occured somewhere around 15,000,000,000 years ago. What if we were to consider the universe a long long time from now ? ...
This page is now getting too large, so I will continue this discussion in a third part. Now we will consider the very limits of numbers that can have meaning in physics !!


Sequential Bayesian estimation and model selection
Work done in collaboration with Tony Pettitt from QUT Brisbane.
I would like to:
- Introduce the Dirichlet form, which can be thought of as a generalisation of expected squared jumping distance, and show that the spectral gap has a variational representation over Dirichlet forms.
- Introduce the asymptotic variance of a Markov chain, which is the theoretical equivalent of the practical measure of 1/effective sample size, and provide a variational representation of this. Amongst other results this leads to a trivial proof of the Peskun ordering.
- Introduce the conductance of a Markov kernel; if this is strictly positive then all sensible asymptotic variances are finite.
Over the last 40 years, Bayesian estimation and model selection has been implemented to address a large variety of complex real-world problems through the use of sophisticated sampling schemes. However, for each stochastic method, there is a computational cost. For our application, the cost of using stochastic techniques is so high that we explore the use of an alternative deterministic method. Through the use of a proposal mechanism we assemble potential models sequentially and in parallel, truncating those with insufficient cumulative evidence. Our model shows big improvements in speed over RJMCMC and also is able to accommodate parameter drift. This was not modelled satisfactorily in the paper of Ridall et al., 2006.Page created on Wednesday, Dec 20, 2017