13 - Mathematics

This course provides students the opportunity to study topics of interest to mathematicians. Subject matter will vary.

A study of the essentials of high school algebra, this course prepares students for further study in mathematics.

This study of basic problem solving introduces the following topics: set theory, mathematical logic, basic counting techniques, probability, and descriptive statistics.

Terms, expressions, functions, and equations; factoring expressions; solving linear equations; solving quadratic equations; using factoring to solve equations; solving exponential and logarithmic equations, graphing functions, absolute value, and applications.

This course provides an analysis of the real number system, functions, graphing, exponential and logarithmic functions, trigonometric functions and topics in analytic geometry.

This course is designed to meet the needs of teachers in the elementary school. Topics include the algebra of matrices, mathematical systems, modular arithmetic, axiomatic systems, systems of numeration, and the nature of proof.

Provides a foundation in algebra and number concepts appropriate for elementary and middle school teachers. Topics include numeration systems, number theory rational numbers, and integers. Emphasis is placed on conceptual understanding, problem solving, mental arithmetic, and computational estimation. A graphing calculator is required; the model is specified by the instructor.

This course is designed to meet the needs of teachers in the elementary school. The course will explore the historical contributions of many different cultures including Egyptian, Greek, Chinese, Indian and others. The course will focus on the development of the notion of numbers and how they have been denoted as well as well as the progression of the development of geometry and algebra.

Provides a foundation in geometry and measurement concepts appropriate for elementary and middle school teachers. This course explores the fundamental ideas of planar and spatial geometry. Content includes the analysis and classification of geometric figures; the study of geometric transformations; the concepts of tessellation, symmetry, congruence, and similarity; and an overview of measurement. The course includes an introduction to the use of Geometer's Sketchpad in the teaching and learning of informal geometry. A graphing calculator is required; the model is specified by the instructor.

A series of workshops intended to enhance the study of Mathematics, Mathematics instruction, or Mathematics history.

A set of workshops that review essential mathematics skills from arithmetic, number theory, algebra, and geometry taught in the elementary schools.

This course will give prospective secondary school mathematics teachers increased proficiency in the mathematical skills and concepts they will teach at the secondary level, helping bridge the gap between the mathematics learned in college and the mathematics taught in high school. Prospective Mathematics for Secondary Education majors must earn an A or B in this course or have earned a Math ACT subscore of 25 or higher to apply for undergraduate admission to the College of Education.

This course provides a study of the concepts in differential calculus, graphs, continuity, differentiation, and applications for algebraic and trigonometric functions. Antiderivatives and definite integrals are introduced at the end of the course.

This course provides a study of the concepts of integral calculus. Applications of the definite integral, exponential and logarithmic functions and methods of integration are studied in detail. Sequences, infinite series, and power series are presented at the end of the course.

This course presents the tools of calculus using applications and models germane to the life sciences.

This course covers concepts of statistics and probability appropriate for elementary and middle school teachers. This course is an introduction to the fundamental principles and procedures of statistical methods, including a study of frequency distribution, measures of central tendency, probability, statistical decision-making, testing hypotheses, estimating, and predicting. Microsoft Excel is used to reinforce major course concepts.

This course provides a study of the concepts in differential and integral calculus, including sequences and series, continuity, limits, differentiation, and integration, with a focus on scientific and engineering applications.  Students use mathematical software packages such as Maple or MATLAB for solving Calculus-based problems.

This course provides a study of Euclidean vector spaces, conic sections, other coordinate systems, parameterized curves and functions of several variables. Differential and integral calculus for functions involving vectors, along with their applications, is presented.

This course focuses on ordinary differential equations. It includes variable separable equations, equations with homogeneous coefficients, exact equations, first order linear equations, applications, homogeneous linear equations with constant coefficients, undetermined coefficients, variation of parameters, power series solutions, linear systems of equations and Laplace transforms.

The study of matrices and matrix algebra, systems of linear equations, matrix inverse and elementary matrices, properties of determinants, vector spaces, especially Rⁿ vectors, linear independence, basis sets, inner products and orthogonality.

This course begins with the Gram-Schmidt process. Other topics of study are Eigenvalues and Eigenvectors, change of basis, linear transformations, diagonalization, symmetrical and similar matrices. Applications of these concepts include quadratic forms and linear programming.

The study of matrices and matrix algebra, systems of linear equations, determinants, and vector spaces with a focus on applications. Topics include LU-decomposition, inner products, orthogonality, the Gram-Schmidt process, and eigenvalue problems. Applications include differential equations, Markov processes, and problems from computer science.

An introduction to discrete structures, this course covers such topics as sets, functions, relations, basic logic, proof techniques, the basics of counting and probability, algorithms, graphs and trees.

This course prepares science students to organize, analyze, visualize, and interpret their data using mathematical techniques. Students learn to use a variety of computer applications to model systems and process measurement data specific to their discipline. They also learn the mathematics that powers these applications.

Random variables, conditional probability and independence, mathematical expectation, discrete and continuous distributions, introduction to estimation theory and hypothesis testing.

The course covers the basic principles of probability and statistics, with applications. Topics include descriptive statistics, the axioms of probability, counting techniques, conditional probability, independence, discrete and continuous random variables, expected value, variation, normal, binomial and Poisson distributions, probability density functions, joint distributions, and point estimation.

A continuation of 13-315. This course covers confidence intervals for mean, proportion, and standard deviation, hypothesis testing, inferences based on two samples, analysis of paired data, analysis of variance, and linear regression and correlation

The study of Euclid’s geometry, its strengths and weaknesses, famous and advanced theorems and its impact on the development of geometry. This latter includes axiomatic systems and proofs, the parallel axiom and the analysis of constructions and transformation geometry.

This course provides a gateway into the more abstract and theoretical expectations of upper-level mathematics courses. The course includes a brief introduction of set theory, symbolic logic, complex numbers, and relations especially as they apply to proof. The course also introduces methods of mathematical proof such as direct proof, indirect proof, proof by contradiction, and proof by induction.

Number theory is the study of the integers. Topics include divisibility, primes, congruences, number theoretic functions, quadratic residues, and primitive roots, with additional topics selected from among Diophantine equations, Pythagorean triples, Fermat's Last Theorem, sums of squares, continued fractions, cryptography, primality testing, and Pell's equation.

The history of Mathematics from the Babylonian period to the early 17th century. The mathematical emphasis is on famous theorems of each era. Biographical information on mathematicians and historical analysis of each era are included.

The history of mathematics beginning with the 17th century to modern time. The mathematical emphasis is on famous theorems of each era. Biographical information on mathematicians and historical analysis of each era are included.

Students examine floating point arithmetic, polynomial interpolation, numerical methods of integration, numerical solution of non-linear equations and numerical linear algebra.

This course provides a formal presentation of the real number system and Euclidean vector spaces (inner products, norms and distance functions), compactness and connectedness, continuity, differentiation, and integration.

A continuation of 13-360, this course studies uniform convergence, sequences and series of functions, differential and integral calculus for functions of several variables, the Implicit Function Theorem and the Inverse Function Theorem.

This course studies sets and their properties, set operations, cardinality, ordered sets, well ordering, finite and infinite sets, and the axiom of choice. Also studied are formal deductive systems especially propositional and predicate logic, properties of deductive systems such as consistency and completeness, and Boolean algebra.

This course studies the process of creating models for real world applications from a wide variety of areas such as physics, chemistry, biology, economics and social sciences. It introduces the students to the basics of mathematical modeling with a focus on model construction, fitting and optimization, analysis, evaluation, and application. This course will make use of computer software in developing models.

A study of complex numbers, analytic functions, integration, power series and calculus of residues is presented.

This course focuses on binary operations, groups, subgroups, permutations, cyclic groups, cosets, and group homomorphisms.

A continuation of 13-440, this course studies rings, fields, Fermat’s Theorem, matrices ideals, ring homomorphisms polynomial rings, vector spaces and linear transformations.

This course provides opportunities for the presentation and discussion of a variety of concepts, principles, literature, and other topics important to the discipline.

This course fulfills the advanced writing requirement for the mathematics major. In this course the student will study a topic related to the algebra, analysis, or statistics sequence required by the mathematics major. The student will complete a written report and an oral presentation based on his/her study.

Students can acquire practical related experience through placement in selected settings. Students submit an internship proposal in advance for approval, maintain a daily task log and submit a five-page written summary report at the conclusion of the internship. A minimum of 210 clock hours and an interview with the on-site supervisor are required.

This course is designed to meet the needs of mathematics majors wishing to study an advanced topic not found in the curriculum.