## MATHEMATICS DIVISION

*UP General Education Program*

**MATH 10. Mathematics, Culture and Society (3)** Appreciation of the beauty and power of mathematics through the examination of its nature, development, utility, and relationship with culture and society. 3 hrs (3 class) PR. None. (1, 2)

*Applied Mathematics*

**AMAT 19. Finite Mathematics (3)** An introduction to the concepts of logic, probability, mathematical programming, theory of games and graph. 3 hrs (3 class). PR. None. (1)

**AMAT 105. Matrices and Applications (3)** Properties, operations and applications of matrices. 3 hs (3 class). PR. MATH 28 or MATH 38. (1,2)

**AMAT 110. Mathematical Modeling (3)** Principles, methods and applications of mathematical modeling. 3 hrs (3 class). PR. MATH 27 or MATH 37. (2)

**AMAT 112. Introduction to Mathematical Optimization (3)** A survey of major techniques in the mathematical modeling of optimization problems. 3 hrs (3 class). PR. MATH 28 or MATH 38 and AMAT 110. (1)

**AMAT 115. Introduction to Mathematical Decision Theory (3)** Fundamental concepts of quantitative decision making. 3 hrs (3 class). PR. AMAT 110 and AMAT 105. (2)

**AMAT 152. Fundamentals of Mathematical Computing (3)** Theory and applications of mathematical computing. 5 hours (2 class, 3 lab). PR. MATH 28 or MATH 38. (1,2)

**AMAT 160. Linear Programming (3)** Formulation, computation, solution and applications of linear programming. 3 hrs (3 class). PR. AMAT 105 and AMAT 110. (1)

**AMAT 161. Non-Linear Programming (3)** Formulation, computation, solution and applications of non-linear programming. 3 hrs (3 class). PR. AMAT 105 and AMAT 110. (2)

**AMAT 162. Integer and Dynamic Programming (3)** Survey of integer and dynamic programming techniques. 3 hrs (3 class). PR. AMAT 160. (2)

**AMAT 163. Metaheuristics (3)** Metaheuristics and their implementation to solve real-world optimization problems. 3 hrs (3 class). PR. AMAT 110. (1)

**AMAT 167. Mathematical Models in Operations Research I (3)** Survey and analysis of mathematical models used in queuing, inventories, maintenance of systems and project management. 3 hrs (3 class). PR. AMAT 110. (1)

**AMAT 168. Mathematical Models in Operations Research II (3) **Survey and analysis of mathematical models used in transportation planning, facility layout and location, finance and investment, and performance evaluation of systems. 3 hrs (3 class). PR. AMAT 160. (2)

**AMAT 170. Theory of Interest (3)** Principles, methods and applications of the theory of interest. 3 hrs (3 class). PR. MATH 37 and AMAT 19. (2)

**AMAT 171. Life Insurance Mathematics I (3) **Mortality, life annuities, life insurance policies and net premiums, methods of valuation, modified and net level reserves, non-forfeiture options, and gross premiums. 3 hrs (3 class). PR. AMAT 170. (1)

**AMAT 172. Life Insurance Mathematics II (3)** Mathematical theory of contingencies of single and multiple lines. 3 hrs (3 class). PR. AMAT 171. (2)

**AMAT 177. Introduction to Mathematical Finance (3) **Introduction to the mathematical theory underlying the pricing and analysis of financial derivatives. 3 hrs (3 class). PR. AMAT 170 and MATH 181. (2)

**AMAT 178. Stochastic Calculus for Finance (3)** The study of Ito processes – their construction, properties and application to the pricing of financial derivatives. 3 hrs (3 class). PR. AMAT 177 and MATH 182. (1)

**AMAT 180. Introduction to Biomathematics (3)** Discrete and continuous mathematical models of biological processes. 3 hrs (3 class). PR. MATH 28 or MATH 38 and AMAT 105. (2)

**AMAT 190. Special Problems (3)** PR. COI. (1,2, M)

**AMAT 191. Special Topics (3).** 3 hrs (3 class). PR. COI. (1)

**AMAT 198. Practicum (3)** (3 class). PR. COI (M)

**AMAT 199. Undergraduate Seminar (1)** PR. COI. (1,2)

**AMAT 200. Undergraduate Thesis. (6)** PR. COI. (1,2, M)1

*Mathematics*

**MATH 18. College Geometry (3) **Axioms and propositions of plane, solid and spherical geometry. 3 hrs (3 class) MATH 14 or MATH 17. (1, 2)

**MATH 20. The Landscape of Mathematics (3)** Fundamental concepts and theorems of mathematics. 3 hrs (3 class). PR. None. (1)

**MATH 25. ****Fundamental Calculus (3)** Fundamental concepts, methods and applications of differential and integral calculus in one or more variables. 3 hrs (2 class, 1 recit). PR. None. (1, 2)

**MATH 27. Analytic Geometry and Calculus II (3)** Differentiation and integration of transcendental functions. Indeterminate forms; integration formulas. Integration procedures. Application of integration. Polar coordinate system. 3 hrs (2 class, 1 recit) PR. None. (1,2, M)

**MATH 28. Analytic Geometry and Calculus III (3)** Parametric equations, vectors and solid analytic geometry; partial differentiation; multiple integrals; infinite series. 3 hrs (2 class, 1 recit). PR. MATH 27. (1, 2, M)

**MATH 36. Mathematical Analysis I (5)** Theory and applications of limits, continuity, and derivatives of functions of a single variable. 5 hrs (5 class) PR. None. (1, 2)

**MATH 37. Mathematical Analysis II (3)** Theory and applications of integrals of functions of a single variable and infinite series. 3 hrs (3 class). PR. MATH 36. (1, 2)

**MATH 38. Mathematical Analysis III (5)** Theory and applications of derivatives and integrals of functions of several variables. 5 hrs (5 class). PR. MATH 37. (1, 2)

**MATH 101. Logic and Set Theory (3) **Elements of mathematical logic and the algebra of propositions; arguments, set operations, functions and relations; algebra of sets; cardinal and ordinal numbers; ordered sets; axiom of choice and other topics in set theory. 5 hrs (2 class, 3 lab). PR. AMAT 19 or MATH 20 and MATH 27 or MATH 37 (1, 2)

**MATH 103. Elementary Theory of Numbers (3) **Divisibility of integers; primes; congruences; quadratic reciprocity; some functions in number theory and diophantine equations. 3 hrs (3 class). PR. MATH 101. (2)

**MATH 111. Modern Algebra I (3)** Fundamental concepts of groups, rings, fields and their substructures; permutation representations; isomorphism theorems. 3 hrs (3 class). PR. MATH 101. (1)

**MATH 112. Modern Algebra II (3)** Advanced topics in the theory of groups, rings and fields including group actions, ring of Laurent series, factorization in commutative rings and Galois theory. 3 hrs (class). PR. MATH 111. (2)

**MATH 115. Introduction to Coding Theory and Cryptography (3) **Algebraic concepts, principles and methods in the construction and analysis of error-correcting codes and ciphers. 3 hrs (3 class). PR. MATH 111. (2)

**MATH 120. Linear Algebra (3)** Properties of modules and vector spaces under linear transformations and their matrices. 3 hrs (3 class) PR. MATH 111. (2)

**MATH 133. Euclidean and Non-Euclidean Geometry (3)** Axiomatic development, concepts, theorems and analytic models of Euclidean and non-Euclidean geometry and their transformations. 3 hrs (3 class) PR. MATH 111. (1, 2)

**MATH 135. Projective Geometry (3)** Basic concepts, principles and theorems of projective geometry and its transformations and collineations, using synthetic and analytic approaches. 3 hrs (3 class) PR. MATH 133 or COI. (1, 2)

**MATH 138. Introductory Topology (3)** Basic topological concepts, theory, and methods. 3 hrs (3 class) PR. MATH 38 and MATH 101. (2)

**MATH 141. Introductory Combinatorics (3)** Elementary Configurations, Enumeration of Configurations and Investigation of Unknown Configurations. 3 hrs (3 class). PR. MATH 38 and MATH 101 or CMCS 56 and CMCS 57. (1)

**MATH 143. Graph Theory (3)** Graphs, Digraphs and Applications. 3 hrs (3 class). PR. MATH 101 or CMCS 56 and CMCS 57. (1)

**MATH 151. Ordinary Differential Equations (3)** Theory methods and applications of ordinary differential equations. 3 hrs (3 class). PR. MATH 38 or MATH 28. (1, 2)

**MATH 152. Partial Differential Equations (3)** Theory, methods and applications of partial differential equations. 3 hrs (3 class). PR. MATH 151. (2)

**MATH 155. Advanced Calculus I (3) **Concepts in the theory of the reals and analysis of functions of one variable. 3 hrs (3 class) PR. MATH 38 and MATH 101 or COI. (1, 2)

**MATH 156. Advanced Calculus II (3) **Concepts in the theory of the real n-space and analysis of functions of several variables. 3 hrs (3 class). PR. MATH 155. (2)

**MATH 160. Vector Analysis (3)** The algebra of vectors; differentiation of vectors; the vector operators del and curl; divergence; Frenet-Serret formulas; involutes, envelops, first and second fundamental forms; geodesics, integration of vectors. 3 hrs (3 class). PR. MATH 28 or MATH 38. (2)

**MATH 165. Complex Analysis I (3) **Fundamental concepts in the analysis of functions of complex variables. 3 hrs (3 class). PR. MATH 133 or COI. (1)

**MATH 166. Complex Analysis II (3)** Advanced concepts in the analysis of functions of complex variables. 3 hrs (class). PR. MATH 165. (2)

**MATH 170. Finite Differences (3) **Calculus of finite differences; difference equations in general; and linear difference equations with constant coefficients and selected topics. 3 hrs (class). PR. MATH 38. (1)

**MATH 174. Numerical Analysis I (3)** Theory, Analysis, and Implementation of Methods in Polynomial Approximation, Numerical Differentiation and Numerical Integration. 3 hrs (class). PR. MATH 38 and AMAT 152 or CMSC 21. (1)

**MATH 175. Numerical Analysis II (3)** Theory, Analysis, and Implementation of Methods in Solving Nonlinear Equations, Linear Systems, and Ordinary Differential Equations. 3 hrs (class). PR. MATH 174. (2)

**MATH 181. Introduction to Probability Theory (3)** Elements of combinatorial analysis and introductory probability theory. 3 hrs (3 class) PR. MATH 101 and MATH 38 or MATH 28. (1, 2)

**MATH 182. Introduction to Stochastic Processes I (3)** Theory and applications of Bernoulli trials; infinite sequence of trials; random walk and run problems; branching processes and Markov chains. 3 hrs (3 class). PR. MATH 181 or STAT 144. (2)

**MATH 191. Special Topics (3). **PR COI. (1)

**MATH 192. Foundations of Mathematics (3)** Axiomatic methods and theories; symbolic logic calculi; school mathematics reform theses; constructivistics, formalistics and related mathematics; various schools of mathematical thought and operationality of their theses. 3 hrs (3 class) PR. COI (2)

**MATH 195. Research Methods in Mathematics (3) **Principles governing mathematical research and documentation. 3 hrs (3 class). PR. MATH 38 and MATH 101. (1, 2)

**MATH 198. Practicum (3)** PR. COI. (M)

**MATH 199. Undergraduate Seminar (1)** 1 hr (1 class). PR. COI. (2)

**MATH 200. Undergraduate Thesis (6)** PR. COI. (1, 2, M)