Spreadsheet: 09b30f93-efb4-4f5c-9f55-19224fb76b1c
Sheet: EXAMPLE

Step 1 |  | LEARNING OUTCOME: Ability to work within theories and with ideas that represent breadth and depth of mathematical science and its applications
 | Education level: | Core Competencies Needed to Grdaute from High Scool | Mathematics: Competencies gained during first two years of study | Baccalaureate Level Mathematics  Competencies | Post-Graduate/ Work Experience Mathematics  Competencies
Step 3/4 | Competency level: | "Knowledge" | "Comprehension" | "Application" | "Analysis" and "Synthesis"
Step 3/4 | Description of competency level for disicpline: | Demonstrate procedural & computational understanding of mathematics. Be able to  solve  problems applying algebraic, geometrical, numeric, statistical, measurement, and probabilistic reasoning.  Be able to  analyze and solve  real world problems. | Expand  upon entry level procedural and computational knowledge to  solve problems in  calculus, linear algebra, differential, equations, discrete mathematics, probability and statistics. Demonstrate the ability to solve real world problems by developing and analyzing simple mathematical and statistical models. | Master  proof techniques in various mathematical theories. In at least one areas of  mathematics and its applications be able y to ask open end questions ,  and  answer them  through mathematical reasoning, computation, and rigorous proof.  Demonstrate proficiency in appling mathematical theories to solve applied problems in various areas. | Be able  to formulate hypotheses,   produce new mathematical knowledge and conduct supervised original research in at least one area of mathematics or its applications.
 | Bloom's Taxonomy Verbs: (This section will not be included in the final copy.) | some "knowledge" verbs: | Bloom Taxonomy:  Conclude, Demonstrate, Discuss, Explain, Generalize, Identify, Illustrate, Interpret, Paraphrase, Predict, Report, Restate, Review, Summarize, Tell Team: Compose, Integrate, Differentiate, Substitute,   Rotate, Reduce, Restrict, Transform,  Continue, Connect, Disconnect, Separate, Estimate,  Project, Trace, …
 |  | some "comprehension" verbs: | Bloom Taxonomy:  Conclude, Demonstrate, Discuss, Explain, Generalize, Identify, Illustrate, Interpret, Paraphrase, Predict, Report, Restate, Review, Summarize, Tell                                                                                                                                                                  Team: Compose, Integrate, Differentiate, Substitute,   Rotate, Reduce, Restrict, Transform,  Continue, Connect, Disconnect, Separate, Estimate,  Project, Trace, …
 |  | some "application" verbs: | Bloom Taxonomy: Apply, Change, Choose, Compute, Dramatize, Interview, Prepare, Produce, Role-play, Select, Show, Transfer, Use Team: Prove, [NAME], Establish (Correspondence), Contradict, Imply, Reverse, Exceed, Minimize, Maximize, Represent,...
 |  | some "analysis" verbs: | Bloom Taxonomy:analyze, select, organize, compare, contrast, illustrate, formualte, deliver, function, direct, break down, correlate, differentiate, discriminate, infer, outline                                                                                                                                                                    Team:
 |  | some "synthesis" verbs: | Bloom Taxonomy: create, design, specify, explain, synthesize, relate, develop, plan, compose, integrate, construct, adapt, organize, execute, aniticpate, collaborate, combine, compile, devise, facilitate, generate, incorporate, modify, reconstruct, reorganize, revise, structure.                                                                                                                                                                                                                  Team:
 |  | some "evaluation" verbs: | Bloom Taxonomy: evaluate, compare, appraise, justify, assess, self-assess, compare and contrast, conclude, criticize, decide, defen, judge, recommend.                                                                                                                                                                                                 Team:
 |  | [NAME] of Mathematical Science and Applications of Mathematical Science
Step 2 | What is it? | At the time  students complete the undergraduate degree requirements, the student should be proficient in comprehension and applying in various working environments contrasting but complementary points of view and perspectives: continuous and discrete, algebraic and geometric,  deterministic and stochastic, theoretical and applied.
 | How does it affect mathematical science | [NAME] and discrete.   Ideas of continuous mathematics laide solid foundation for many mathematical theories and applications (calculus, differential equations, analysis) and remain crucially important as the language of science and economics. However, with development of computer science and computational power of modern civilization, discrete mathematics, matrix algebra, probability and statistics, and other topics, that are not based on the ideas of continuity,   start playing a crucial role in application and create  a lot of theoretical challenges.
 |  | Algebraic and geometric.  Most mathematically related arguments are, in one way or another, related to algebra, algebraic computations and techniques.  Algebra laid a foundation for studying various areas of mathematics and its applications.  Geometry was for centuries the heart of mathematics and continues to be  a vital part of it. Geometric thinking and visualization, effective use of graphics software to enhance understanding are important aids to problem solving and scientific/engineering discovery.  As represented in the [NAME] theory, algebraic geometry, dynamical systems, Riemannian geometry and other research areas, it is a central part of the research enterprise.” ([NAME], [NAME], “Two Critical Issues for the Math Curriculum,” in CUPM Discussion Papers about Mathematics and the Mathematical Sciences in 2010: What Should Students Know?, MAA Reports, 2001.Quote p. 46). Discrete  geometry and finite geometry recently received  a lot of attention  from mathematicians and specialists from different areas because of its importance to applications.
 |  | Deterministic and stochastic.  Deterministic models are among the glorious achievements of mathematics, but stochastic methods are just as valuable as deterministic. Modern mathematics and its applications  rely on fields that use data analysis and effectively  conclude  from data. In modern world it is equally important to master approaches that are deterministically driven and data-driven.
 |  | Theoretical and applied.  The theoretical ideas of mathematics are in the heart of mathematical sciences and play a crucial role in  understanding  the coherence, the beauty,  the power of the discipline, as well as in discovering opportunities to apply mathematical methods to solve  applied problems. Recent advances in  mathematical sciences and in technology have implications for the balance between the theoretical and the applied in the undergraduate major.  Mathematical methods are applicable to almost every area of human activities, that include but are not limited to engineering, science, economics, medicine, etc.