Geometry and Discrete Mathematics - Free ebook download as PDF File (.pdf), Text File (.txt) or read book online for free. Math by Subject K12 Topics algebra arithmetic calculus discrete math geometry pre-calculus prob/stat Advanced Topics. Geometry And Discrete Mathematics 12.

• Discrete Differential Geometry

MATH 129-Analytic Geometry and Calculus I (4 credits). The first calculus course in a three-course sequence. Intended primarily for chemistry, computer science, or mathematics majors. Topics include equations; inequalities; analytic geometry; trigonometric functions; an introduction to exponential and logarithmic functions; limits; continuity; derivatives; differentials; maxima and minima problems; graphing techniques; the defi nite integral. Prerequisite: CORE 098 Mathematical skills.

Offered Fall semesters. MATH 235-Discrete Mathematics (3 credits).

A survey of some of the fundamental ideas of discrete mathematics. Topics include set theory, relations on sets (especially equivalence relations, partial orders, and functions), number theory, induction and recursion, combinatorics, and graph theory. Prerequisite: MATH 127 and MATH 130 or approval of the Department Chairperson. Offered Fall semesters.

MATH 236 Geometry MATH 237 Mathematics for the Physical Sciences I MATH 238 Mathematics for the Physical Sciences II MATH 250. MATH 363-Mathematical Modeling (3 credits). Topics in game theory include: games with perfect information; Nash equilibrium, mixed strategy equilibrium, Bayesian games; games with imperfect information; and repeated games. Topics in curve fi tting include: curve fi tting with polynomials; Hermite method, Lagrange method, least-squares method; interpolation with piecewise polynomial functions;curve fitting with splines; and smoothing techniques. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years. MATH 425-Abstract Algebra (3 credits).

Emphasis on students formulating and testing their own conjectures. Topics include groups; cyclic groups; subgroups; direct products; cosets; normal subgroups; quotient groups; homomorphisms; rings; subrings; ideals; ring homomorphisms; fields. Approval of the Department Chairperson is required. Offered Fall semesters. STATISTICS MINOR 6 Courses Take Name MATH 129 Calculus I MATH 130 Calculus II MATH 231 Calculus III MATH 361 Probability Choose one MATH 124 Probability & Statistics for Education MATH 126 Introduction to Statistics MATH 128 Introduction to Statistics, Data Analysis, and Applications to Life Science MATH 362 Statistics Choose one additionally MATH 124 Probability & Statistics for Education MATH 125 Calculus MATH 126 Introduction to Statistics MATH 127.

MATH 129-Analytic Geometry and Calculus I (4 credits). The first calculus course in a three-course sequence. Intended primarily for chemistry, computer science, or mathematics majors. Topics include equations; inequalities; analytic geometry; trigonometric functions; an introduction to exponential and logarithmic functions; limits; continuity; derivatives; differentials; maxima and minima problems; graphing techniques; the defi nite integral. Prerequisite: CORE 098 Mathematical skills. Offered Fall semesters. MATH 235-Discrete Mathematics (3 credits).

A survey of some of the fundamental ideas of discrete mathematics. Topics include set theory, relations on sets (especially equivalence relations, partial orders, and functions), number theory, induction and recursion, combinatorics, and graph theory. Prerequisite: MATH 127 and MATH 130 or approval of the Department Chairperson. Offered Fall semesters. MATH 236 Geometry MATH 237 Mathematics for the Physical Sciences I MATH 238 Mathematics for the Physical Sciences II MATH 250.

MATH 363-Mathematical Modeling (3 credits). Topics in game theory include: games with perfect information; Nash equilibrium, mixed strategy equilibrium, Bayesian games; games with imperfect information; and repeated games.

Topics in curve fi tting include: curve fi tting with polynomials; Hermite method, Lagrange method, least-squares method; interpolation with piecewise polynomial functions;curve fitting with splines; and smoothing techniques. Prerequisite: MATH 231 or approval of the Department Chairperson. Alternate years.

Math 126 Number Theory Math 126 Number theory BP 322, 793-7421 Spring 2006 This course page is obsolete. I'll prepare a new page next time I teach the course.

General description. Math 126 introduces number theory and trains students to understand mathematical reasoning and to write proofs. It includes the unique factorization of integers as products of primes, the Euclidean algorithm, Diophantine equations, congruences, Fermat's theorem and Euler's theorem and some applications such as calendar problems and cryptology. Prerequisites. The prerequisite for the course is either one semester of Discrete Mathematics Math 114, or one semester of calculus (Math 120 or Math 124).

Others by permission. Course goals and objectives. The primary goal, of course, is to introduce the theory of numbers.

Although this is an introductory course to the subject, the approach is rigorous, and many of the concepts are subtle and deep. Students will learn some of the history of the theory of numbers, see the importance and uncertainty of conjectures, learn methods of computation in number theory and investigate conjectures, follow deductive proofs of many of the theorems in the subject, and develop and write up some of their own proofs. An Introduction to Number Theory by Harold Stark, published by. Course Hours. MWF 11:00-11:50. Survey of the subject.

The concepts of divisibility, Diophantine equations. The prime number theorem. Pythagorean triples. Various conjectures.

Survey of., even and odd numbers, the Euclidean algorithm, least common multiple., irrational numbers., infinitude of primes, propositions on even and odd numbers, sum of a geometric progression, perfect numbers. Pythagorean triples.

Axioms of number theory. Mathematical induction. Notes on. Elementary properties of divisibility. Remainder theorem.

The Euclidean algorithm Greatest common divisors. Relatively prime numbers. Introduction to continued fractions. The fundamenatal theorem of arithmetic: the unique factorization theorem. Irrationality of surds.

Multiplicative functions: number of divisors, sum of the divisors Perfect numbers and Linear Diophantine equations. Congruences modulo n. Fundamental properties of congruences, residue systems.

Linear congruence equations, Chinese remainder theorem. Reduced residue systems and Euler's totient (phi) function, Euler's theorem and Fermat's theorem, pseudoprimes. Primitive roots. Public-key cryptography. Diophantine equations.

Congruences in solving Diophantine equations. Introduction to Pell equations. Pythagorean triples, Fermat's method of descent. Larry Freeman's.

Discrete Differential Geometry

Numbers, rational and irrational. Repeated decimals. Statement of Liouville's theorem, transcendental numbers. Continued fractions from a geometric viewpoint. The continued fraction algorithm. The best approximations to rational and irrational numbers. Periodic continued fractions.

The Fermat-Pell equation and the continued fraction expansion of square roots. Assignments & tests. There will be numerous short, mostly from the text, occasional quizzes, two tests during the semester, and a two-hour final exam during finals week.

Course grade. The course grade will be determined as follows: 2/9 assignments and quizzes, 2/9 each of the two midterms, and 1/3 for the final exam. Class notes Homework exercises.

Recursive solutions to Pell equations. Newton's method.

Pell equations. Meeting 37.

Comments on continued fractions. Meeting 36. Harmonic theory. Meeting 34. More on continued fractions. Meeting 33. Introduction to continued fractions.

Second test, Wednesday, Apr. Writing up proofs; decimal fractions. Meeting 28. Decimal expansion of rational numbers.

More on Pythagorean triples. Fermat's method of descent. Pythagorean triples. Diophantine equations.

Fermat/Wiles theorem. Meeting 23. More on public-key cryptograpy. Public-key cryptography, the mathematics behind the RSA algorithm. The group of totatives, the order of a totative, primitive roots.

Fermat's little theorem and Euler's theorem. Multiplicativity of Euler's phi function.

Meeting 19. Exercises on congruence and CRT.

Totatives and Euler's phi function. Linear congruences, the Chinese remainder theorem.

First test, Wednesday, Feb. Meeting 14. Linear congruences.

N, Z, Q, R, C, Z n, squares modulo n. Polynomials and congruence.

Congruence modulo n. Linear Diophantine equations. Divisors of a number, their number and their sum. Multiplicative functions. Perfect numbers. Irrationality of surds.

The unique factorization theorem. More on divisibility, the Euclidean algorithm, and greatest common divisors. Some elementary properties of divisibility, prime numbers, greatest common divisors, and the Euclidean algorithm. What are numbers and what should they be? An Innocent Investigation. 13, due Mon, Apr 3, from page 161, one of the exercises 3, 5 completely.

12, due Fri, Mar 31, from page 155, one of the exercises 1, 2, 7 completely. 11, due Fri, Mar 14, from page 148, exercises 1, 4; and from page 151, exercises 3, 7, 11. 10, due Fri, Mar 17, from page 106, exercises 2, 4, 5, 9; and from page 108, misc. Exercises 8, 15.

9, due Fri, Mar 3, from page 82, exercises 1, 2, 4, 10; and from page 86, exercises 1, 2, 6, 7. 8, due Wed, Mar 1, from page 76, exercises 1-3, 7-9, 11-13, 17, 20.

7, due Fri, Feb 17, from page 54, exercises 1-5, 8, 10; and from page 63, exercises 1, 4-6, 8, 9, 13, 19-21. 6, due Wed, Feb 15, from page 47, exercises 3-8, 10. 5, due Fri, Feb 10, from page 43, exercises 2, 3, 5, 6, 7. 4, due Wed, Feb 8, from page 35, exercises 1, 2. 3, due Mon, Feb 6, from page 32, exercises 5, 7, 12, 13, 15.

2, due Wed, Feb 1, from page 26, exercises 2, 3, 4, 5, 6, 11, 12, 13. 1, due Wed, Jan 25, from page 14, Misc. Exercises: 1, 2, 3, 4. This page is located on the web.