Bachelor of Science in Mathematics

**MATH 111 Fundamentals of Mathematics (Cr. 3)**

This is a basic math course for non-science students which covers problem solving techniques, sets, basic probability and statistics, number systems and their structure, linear and quadratic equations, basic consumer mathematics.

**MATH 141 Calculus and Analytic Geometry I (Cr. 4)**

The first course in calculus covers functions and their graphs, limits and continuity, tangent lines and derivatives, some theorems on differentiation, applications of derivatives, such as: curve sketching, maxima and minima problems, definite and indefinite integrals, and applications of integrals.

**MATH 142 Calculus and Analytic Geometry II (Cr. 4)**

This course is a continuation of Math 141 and includes methods of integration and applications. Other topics covered are: inverse trigonometric, logarithmic and exponential functions, other transcendental functions, conic sections, parameterized curves and polar coordinates, some sequences and series.

**Prerequisite: MATH 141**

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**MATH 234 Differential Equations (Cr. 3)**

This course introduces various types of ordinary differential equations, first and higher order, linear systems of equations, Laplace transform and power series solutions, and some physical applications.

**Prerequisite: MATH 142**

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**MATH 235 Introduction to Linear Algebra (Cr. 3)**

This course covers fields, linear systems over fields, matrices and their arithmetic, determinant of a matrix, linear spaces and subspaces, bases, linear transformations, eigenvalues and eigenvectors, diagonalization and canonical forms.

**Prerequisite: MATH 142**

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**MATH 238 Discrete Mathematics (Cr. 3)**

This course introduces students to logic, set theory and proof techniques, relations functions and their properties, mathematical induction, cardinality, basic concepts in number theory, combinatorial mathematics, and methods of counting.

**Prerequisite: MATH 142**

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**Math 239 Mathematics for CAIS students (Cr. 3)**

This course introduces logic and methods of proof, sets and set operations, relations and functions, mathematical induction and recursion, introduction to matrices and solving simultaneous equations in several variables, methods of counting, introduction to trees and graphs.

**Prerequisite: MATH 142**

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**MATH 241 Calculus and Analytic Geometry III (Cr. 4)**

This course incorporates further work in calculus and analytic geometry covering vectors and analytic geometry in space, vector functions with their derivatives, multivariable functions, partial differentiation and multiple integration and applications, and some vector analysis.

**Prerequisite: MATH 142**

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**MATH 331 Probability (Cr. 3)**

This course introduces probability, methods of enumeration, conditional probability and independence, random variables of discrete and continuous types, expectation and variance, different kinds of distributions, moment generating function and functions associated with the normal distribution, and the central limit theorem.

**Prerequisite: MATH 241 (MATH 238 highly recommended)**

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**MATH 332 Theory of Numbers (Cr. 3)**

This course studies integers, divisibility properties, primes, prime factorization, diophantine equations, numerical functions, congruences and their applications, residues, primitive roots, theorems of Euler, Fermat, Lagrange, Wilson and the Chinese Remainder theorem.

**Prerequisite: MATH 142 and MATH 238.**

**MATH 333 Mathematical Statistics (Cr. 3)**

This isa continuation of MATH 331 which includes an introduction to sampling theory, the student t and F distributions with random functions associated with them, and the law of large numbers. Estimation theory, which includes unbiased, consistent, efficient, sufficient and maximum likelihood estimators is also included as well as testing hypothesis for means, proportions, variances and some regression.

**Prerequisite: MATH 331**

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**MATH 334 Advanced Calculus I (Cr. 3)**

This course gives a formal introduction to the real number system, sequences of real numbers and their limits, continuity and differentiability of functions of a real variable, uniform continuity, approximation of functions by polynomials, Taylor's Theorem.

**Prerequisite: MATH 241, MATH 238.**

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**MATH 335 Advanced Calculus II (Cr. 3)**

This course is a continuation of Math 334 and includes Riemann integration, series of real numbers, sequences and series of functions, point wise and uniform convergence, power series and analytic functions.

**Prerequisite: MATH 334**

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**MATH 336 Introduction to Modern Algebra ****(Cr. 3)**

This is an introductory course in the elements of modern algebra and includes: groups, homomorphism, Lagrange theorem, quotient groups, isomorphism theorem, symmetric groups, rings, ideals, quotient rings and homomorphism, rings of polynomials over integral domains, principal ideal domain and the unique factorization theorem, extension of fields, algebraic and transcendental functions.

**Prerequisite: MATH 241, MATH 238 (MATH 235 highly recommended).**

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**MATH 337 Topology (Cr. 3)**

Metric spaces, convergence and continuity, completeness and Cauchy’s completion theorem, general topological spaces, separation axioms, metrizability, compactness, and connectedness, compactification theorems, product spaces and Tychonof theorem, the fundamental group and an introduction to homotopy theory are included in the course.

**Prerequisite: MATH 335**

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**MATH 338 Complex Variables (Cr. 3)**

The algebra and geometry of complex numbers, analytic functions, Cauchy-Riemann Equations, complex series, integration of complex functions, and some applications of complex variables to physics are covered in the course.

**Prerequisite: MATH 335**

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**MATH 341 Multivariable Calculus (Cr. 3)**

The Euclidean spaces and elementary topology on them, limits and continuity, differentiability of real and vector valued functions, implicit and inverse function theorems, measure and integrals in Euclidean spaces are covered in the course.

**Prerequisite: MATH 335**

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**MATH 342 Topics in Algebra (Cr. 3)**

This course is a continuation of MATH 235 and MATH 336 which includes: inner product spaces, orthonormal bases and the Grahm-Schmidt process, linear operators on inner product spaces, unitary and Hermitian operators, the spectral theorem, bilinear and quadratic forms, diagonalization, Sylvester’s and Caley-Hamilton theorems, Jordan forms; extension of fields and an introduction to Galois theory.

**Prerequisite: MATH 235, MATH 336**

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**MATH 352 Introduction to Statistics (Cr. 3)**

The course is a service course. It is intended to provide an introduction to elementary statistical concepts basic to interpretations and applications. The first part of the course is descriptive statistics and the second part is inferential, tests for means proportions, contingency tables, correlation and linear regression are studied. A computer statistical package is used for data analysis.

**MATH 361 Regression Analysis (Cr. 3)**

Sampling techniques, testing statistical hypothesis, single and multiple linear regressions, polynomial and nonlinear regression, model building and statistical inference in regression analysis are covered in the course. A computer statistical package is used for data analysis.

**Prerequisite: MATH 333**

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**MATH 362 Topics in Applied Statistics (Cr. 3)**

This course is an introduction to basic methods of experimental design, analysis of variance, contingency tables, and nonparametric statistical techniques such as: the sign test, Wilcoxon and other tests. A computer statistical package to utilize these methods will be used.

**Prerequisite: MATH 361**

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**MATH 371 Applied Mathematics (Cr. 3)**

Fourier series and their applications, orthogonal and periodic functions, Parseval equation, partial differential equations, heat and wave equations are covered in this course. Fourier transforms and some topics in calculus of variation are also covered.

**Prerequisite: MATH 234 (MATH 235 highly recommended)**

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**MATH 372 Numerical Analysis (Cr. 3)**

Solutions of equations in one variable, polynomial approximation, numerical differentiation and integration, initial value problems for ordinary differential equations, linear systems, iterative technique, and numerical solutions to partial differential equations are covered in the course.

**Prerequisite: MATH 234 (MATH 235 highly recommended)**

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**MATH 389 Senior Seminar in Mathematics (Cr. 1)**

Senior mathematics majors are required to conduct an intensive research study of a particular subject in mathematics chosen from a selected list of topics approved by the Mathematics Department. Seminar participants must present their subjects for discussion at seminar meetings with faculty members.

**Required of and restricted to senior mathematics majors**

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**MATH 399 Special Topics in Mathematics (Cr. 3)**

This is an independent study course open to senior mathematics majors. Topics are selected by the instructor in accordance with the student’s ability and previous study.

**Prerequisite: Consent of Department**

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