Major in Mathematics

## Mathematics

### Course Descriptions

**MAT 100 – Basic Mathematics**

(1–2) F,S,U

Review of arithmetic and algebra: number systems, operation with signed numbers, fractions, decimals and percents, exponents, radicals, operations with algebraic expressions, factoring, linear equations, solutions of word problems. Two credits during regular semesters and one credit during Summer Institute. Admission by Mathematics Placement Test.

**MAT 104 – Intermediate Algebra**

(3) F,S,U

Operations with polynomials, solution of equations and verbal problems, exponents and radicals, quadratic equations, systems of linear equations, graphing techniques. Mathematics 104 may not be taken for credit after receiving a C or better grade in Mathematics 151 or above. Prerequisites: Mathematics 100, or satisfactory performance in Mathematics Placement Test administered by mathematics department, or permission of instructor.

**MAT 107 – Introduction to Mathematics**

(3) F,S,U

Basic principles and techniques of mathematics. May include theory of sets, logic, number theory, geometry, probability and statistics, consumer mathematics. Emphasis on unity of thought and consistency of approach to problem solving. History and relevance of mathematics for the growth of civilizations. Prerequisite: completion of mathematics requirement in component one of core.

**MAT 112 – Basic Statistics**

(3) F,S,U

For non-mathematics majors. Probability theory topics, binomial distribution, normal distribution, descriptive statistics, frequency distribution, measures of central tendency, hypothesis testing. Confidence intervals, correlation, and prediction. Prerequisite: completion of mathematics requirement in component one of core. Students may not also take for credit Psychology 211, Economics 241, or Sociology 211.

**MAT 131 – Plane Trigonometry**

(3) IR

Trigonometric functions, identities, related angles, degree and radian measure, graphs, compound and multiple angles, equations, inverse functions, oblique triangles, complex numbers, DeMoivre’s Theorem. Prerequisite: competence in algebra at intermediate level or permission of instructor.

**MAT 143 – Mathematical Analysis for Business and Economics I**

(3) F,S

For business and economics majors. Topics include algebra, analytic geometry, applications, elements of linear programming, and mathematics of finance. Prerequisites: Mathematics 104, or satisfactory performance in Mathematics Placement Test administered by mathematics department, or permission of instructor.

**MAT 144 – Mathematical Analysis for Business and Economics II**

(3) F,S

Continuation of Mathematics 143. Topics include functions in business and economics, fundamentals of differential and integral calculus with selected applications. Prerequisite: Mathematics 143.

**MAT 151 – Pre-Calculus**

(3) F,S

Elementary functions and their graphs including polynomial, rational, exponential, logarithmic and trigonometric functions, quadratic curves, and introduction to analytic geometry. Prerequisites: Mathematics 104, or satisfactory performance in Mathematics Placement Test administered by mathematics department, or permission of instructor.

**MAT 201 – Calculus I**

(3) F,S

Review of analytic geometry and trigonometric functions. Limits, derivatives, maxima and minima, related rates, graphs, differentials, mean value theorem. Prerequisite: Mathematics 151 or satisfactory performance in calculus readiness test administered by mathematics department.

**MAT 202 – Calculus II**

(3) F,S

Indefinite integration, definite integrals and applications; logarithmic, exponential, hyperbolic functions and their inverses, l’Hopital’s rules; improper integrals and methods of integration. Prerequisite: Mathematics 201.

MAT 300 - Selected Topics

MAT 300 - Selected Topics

(1-3) IR

**MAT 301 – Calculus III**

(3) F

Vectors, parametric equations, polar coordinates, infinite series, elementary differential equations. Prerequisite: Mathematics 202.

**MAT 302 – Calculus IV**

(3) S

Analytic geometry of three dimensions, functions of more than one variable, partial differentiation, multiple integrals, line and surface integrals. Prerequisite: Mathematics 301.

**MAT 303 – History of Mathematics**

(3) S

Study of mathematical concepts in historical perspective. Lives, character, and contributions of the mathematicians and the relation of mathematics to other sciences. Prerequisite: Mathematics 202 or permission of the instructor.

**MAT 305 – Fundamental Structures of Mathematics**

(3) F

Logic, sets, relations, functions, cardinal numbers, algebraic systems. Emphasis on concepts and methods of proof. Prerequisite: Mathematics 202 or permission of instructor.

**MAT 313 – Mathematics: A Heuristic Approach**

(3) F

Historical and developmental perspectives. Problem solving and pattern recognition. Motivational techniques. Practical applications, emphasis on knowledge and understanding of subject matter. Diagnostic tools to detect and correct common misconceptions. Assessment and statistical interpretation of errors. Prerequisite: Mathematics 305 or Computer Science 201 and Computer Science 301 or permission of the instructor.

**MAT 317 – Ordinary Differential Equations**

(3) O

First and second order differential equations, linear equations of higher order, power series solutions. Existence of solutions. Systems of differential equations. Applications of differential equations. Prerequisite: Mathematics 301.

**MAT 321 – Probability and Statistics**

(3) O

Mathematical models of random experiments, discrete and continuous random variables. Bivariate and multivariate distributions. Prerequisite: Mathematics 301.

**MAT 322 – Mathematical Statistics**

(3) IR

Random sampling, The Central Limit Theorem, estimation of parameters, confidence intervals, tests of hypotheses, least squares, regression, and contingency tables. Prerequisite: Mathematics 321.

**MAT 331 – Linear Algebra**

(3) F

Systems of linear equations, matrices, determinants, vectors, vector spaces and subspaces, linear independence, basis and dimension, orthonormal bases, Gram-Schmidt process, eigenvalues and eigenvectors, diagonalization, linear transformations, applications. Prerequisite: Mathematics 202 or permission of instructor.

**MAT 334 – Introduction to Abstract Algebra**

(3) S

Elementary theory of groups, rings, domains, and fields, including the integers and polynomial rings and their applications. Quaternians and the Cayley numbers. Prerequisites: Mathematics 305 with grade of C or better, or permission of instructor.

**MAT 341 – Number Theory**

(3) IR

Topics include prime numbers, greatest common divisors, congruences, Wilson’s, Fermat’s and Euler’s Theorems, polynomial congruences, perfect numbers, primitive roots, indices, quadratic residues, Legendre symbol, quadratic reciprocity law. Prerequisite: Mathematics 305 or permission of instructor.

**MAT 351 – Euclidean and non- Euclidean Geometries**

(3) IR

Euclidean geometry examined as a system of carefully formulated axioms, precise definitions, and rigorous proofs of theorems in plane and solid geometry. History, foundation, and applications of the non-Euclidean geometries: Lobatchevskian and Riemannian. Prerequisite: Mathematics 305 or permission of instructor.

**MAT 390 – Independent Study**

(1–3) IR

**MAT 400 – Topics in Higher Mathematics**

(3) IR

In-depth discussion of current problems and developments in particular branch of mathematics. Content may vary according to specialty of instructor. May be repeated once. Permission of instructor required.

**MAT 401 – Real Analysis I**

(3) O

Foundations of the real number system, functions and sequences, limits, continuity and differentiability. Prerequisites: Mathematics 302 and 305 or permission of instructor.

**MAT 402 – Real Analysis II**

(3) IR

Integration, series, uniform convergence. Additional topics may include: transformations in Euclidean spaces, Fourier series, metric spaces and principles of general topology. Prerequisite: Mathematics 401.

**MAT 413 – Mathematics: A Heuristic Approach: Practicum**

(4) Y

Students apply the principles learned in Mathematics 313 in a Mathematics 100 classroom, participating in planning, preparation, presentation, and assessment. Discussion and analysis. Daily journal required. Prerequisite: Mathematics 313. By invitation only.

**MAT 484 – Complex Variables**

(3) IR

Analytic functions. Harmonic functions. Cauchy’s Theorem, Cauchy Integral formula, series representations of analytic functions, calculus of residues, conformal mappings, applications. Prerequisite: Mathematics 401.

**MAT 486 – Numerical Analysis I**

(3) IR

Iteration, interpolation, and approximation. Numerical solutions of equations and systems of equations. Numerical differentiation and integration. Prerequisites: Mathematics 302 and Computer Science 101, or permission of instructor.

**MAT 487 – Numerical Analysis II**

(3) IR

Difference equations. Numerical solutions of differential equations. Approximations by spline functions. Least squares approximation. Prerequisite: Mathematics 486.

**MAT 490 – Independent Study**

(1–3) IR

**Note:**The figure in parentheses following the title of the course indicates the credit hours per term. Courses that extend through two terms are shown as follows: (3, 3). Courses that are one term only are shown by: (3). Courses with variable credit are shown with the range of credit available, for example: (1-6).

Letters appearing after course credit hours in this section are explained as follows:

S=Spring

IR=irregularly

F=Fall

U=Summer Session

Y=at least once each academic year Check schedule for Winter Session

O=every other year

The College reserves the right to cancel any course if registration does not justify continuance and to make changes in curricula at any time.