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. (2)

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. (1)

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)

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 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)