Pell and Pell Lucas numbers with applications Pell and Pell Lucas Numbers has been carefully crafted as an undergraduate graduate textbook; the level of which depends on the college university and the instructors preference. The exposition moves from the basics to more advanced topics in a systematic rigorous fashion motivating the reader with numerous examples figures and exercises. Only a strong foundation in precalculus plus a good background in matrices determinants congruences and combinatorics is required. The text may be used in a variety of number theory courses as well as in seminars workshops and other capstone experiences for teachers in training and instructors at all levels. A number of key features on the Pell family surrounds the historical flavor that is interwoven into an extensive in depth coverage of this unique text on the subject. Pell and Pell Lucas numbers like the well known Fibonacci and Catalan numbers continue to intrigue the mathematical community with their beauty and applicability. Beyond the classroom setting the professional mathematician computer scientist and other university faculty will greatly benefit from exposure to a range of mathematical skills involving pattern recognition conjecturing and problem solving techniques; these insights and tools are presented in an array of applications to combinatorics graph theory geometry and various other areas of discrete mathematics. Pell and Pell Lucas Numbers provides a powerful tool for extracting numerous interesting properties of a vast array of number sequences. It is a fascinating book offering boundless opportunities for experimentation and exploration for the mathematically curious from student to the professional amateur number theory enthusiast and talented high schooler.