# Math & Computer Science Department B.S. Mathematics Course Descriptions

### B.S. Mathematics Course Descriptions

By creating, using, and interpreting graphs, students will investigate real world applications of linear, exponential, power, and logarithmic functions. Topics will include scientific notation, units and significant figures, curves and data, and systems of equations. Not open to students who have credit for any other mathematics course.

Illustrations of contemporary uses of mathematics, varying from semester to semester, frequently including topics from: graph theory, theory of apportionment, voting theory and methods, counting methods, probability, personal finance, and game theory.

A study of sets, counting techniques, basic probability theory, stochastic processes, random variables, probability distributions, descriptive statistics, matrices, and linear systems of equations. Emphasis is on mathematical model comprehension and problem solving in the areas of business and the life and social sciences.

Elementary set theory, number theory, an intuitive development of the real number system, and basic concepts of algebra, measurement, intuitive geometry, functions, probability and statistics.

Functions and graphs, exponential and logarithmic functions, trigonometric functions. The emphasis is on topics and concepts that are needed in mathematics, science, or business. Applications play a central role and lead to graphing, data analysis, and modeling.

An introduction to the concepts of differentiation and integration with emphasis on their applications to solving problems that arise in business, economics, and social sciences.

Differential and integral calculus of functions of a single real variable, including trigonometric, exponential, and logarithmic functions. The course will cover limits, continuity, differentiation, applications of derivatives, introduction to integration, techniques of integration and the fundamental theorem of calculus. Derivatives and integrals are explored graphically, symbolically, and numerically.

Applications of integration, sequences, series, power series, Taylor’s Theorem, and elementary differential equations. Vectors and geometry in space. The dot and cross products, lines, planes, surfaces in space and cylindrical and spherical coordinates.

An introduction to mathematical proof. Topics to include elementary symbolic logic, mathematical induction, algebra of sets, finite probability, relations, functions, and countability.

Systems of linear equations and matrices, determinants, vector spaces and inner-product spaces, linear transformations, eigenvalues and eigenvectors. The emphasis is on computational techniques and applications.

Calculus of vector functions, including functions of several variables, partial derivatives, gradients, directional derivatives, maxima and minima. The course will also cover multiple integration, line and surface integrals, Green’s Theorem, Divergence Theorems, Stokes’ Theorem, and applications.

A study of the theory of interest and its applications. Topics include compounding, nominal and effective rates of interest, force of interest, valuation of annuities, amortization, bond valuation, asset liability management, and derivative investment.

Set functions, events, addition and multiplication rules, combinatorial probability, conditional probability and independence, Bayes Theorem, discrete distributions, continuous distributions, multivariate distributions, transformations, expectation and moments, moment generating functions, and the Central Limit Theorem.

First order and second order linear differential equations, systems of differential equations, numerical methods and series solutions. Applications and the development of mathematical models.

Operations with complex numbers, derivatives, analytic functions, integrals, definitions and properties of elementary functions, multivalued functions, power series, residue theory and applications, conformal mapping.

Survey of mathematical methods for engineers and scientists. Ordinary differential equations and Green’s functions; partial differential equations and separation of variables; special functions, Fourier series; complex integrals and residues; distribution functions of probability. Applications to engineering and science.

Incidence and and geometry, parallel postulates, Euclidean and non-Euclidean geometry. Models and the development of Euclidean geometry.

Basic principles of counting: addition and multiplication principles, enumeration techniques, including generating functions, recurrence formulas, rook polynomials, the principle of inclusion and exclusion, and Polya’s theorem. This course will also cover basic concepts of graph theory: graphs, digraphs, connectedness, trees and graph colorings.

Algorithm behavior and applicability. Interpolation, roots of equations, systems of linear equations and matrix inversion, numerical integration, numerical methods for ordinary differential equations, and matrix eigenvalue problems.

The major mathematical developments from ancient times to the 21st century. The concept of mathematics, changes in that concept, and how mathematicians viewed what they were creating.

Introduction to elementary additive and multiplicative number theory, including divisibility properties of integers, congruence modulo n, linear and quadratic congruences, some Diophantine equations, distribution of primes, and additive arithmetic problems.

An introduction to groups, homomorphisms, cosets, Cayley’s Theorem, symmetric groups, rings, polynomial rings, quotient fields, principal ideal domains, and Euclidean domains.

Set theory, topological spaces, metric spaces, continuous functions, separation, cardinality properties, product and quotient topologies, compactness, connectedness.

The real number system, sequences, limits and continuity, differentiation, integration, sequences of functions, infinite series and uniform convergence.

Techniques for attacking and solving challenging mathematical problems and writing mathematical proofs.

Investigation of some topic in mathematics to a deeper and broader extent than typically done in a classroom situation.

A continuation of “MTH-4910. At the conclusion of the course, results will be given in both a written paper and an oral presentation to the seminar participants and the department faculty.

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