Undergraduate Major Mathematics (BA)

Calculus is the mathematical study of change that has widespread applications in science, engineering, economics and business. This course provides a rigorous introduction to single-variable calculus. Topics include limits, continuity, differentiation and integration of algebraic, trigonometric, exponential, and logarithmic functions, applications of derivatives, and integration, including the Fundamental Theorem of Calculus. This course will encourage students to think beyond memorizing formulas and to work towards understanding concepts.

This course is a continuation of MAT 225 that deepens a student's understanding of single-variable calculus. Students will learn new techniques of integration, including substitution, integration by parts, partial fractions, and integration tables. This course will also extend a student's knowledge of addition. That is, students already know how to add two, three, or n numbers together but, in this course they will learn how to add an infinitely many numbers together. This will enable students to represent differentiable functions-including exponential, trigonometric and logarithmic functions-as functions that look like polynomials with infinitely many terms. In doing so, students will enhance their abilities to evaluate and estimate integrals. Finally, students will also learn about parametric curves and polar coordinates-both useful tools for describing the motion of moving objects such as projectiles, planets, or satellites-in order to apply single-variable calculus skills in additional settings. Students may not take both MAT 211 and MAT 275 for credit.

This course introduces students to the language and methods used to create and write mathematical proofs and solve problems. Methods of proof will include: direct, contrapositive, contradiction, and induction. Methods of problem solving will be based on Polya's four steps for problem solving. Students will learn about and utilize the many functions of proof including: verification, explanation, communication, discovery, justification, and inquiry. The course will also explore the relationship between problem solving and the process of proving. Students will explore fundamental abstract concepts in mathematics including: functions and relations, set theory, number theory, and logic.

Many real-world applications of calculus in science, engineering, economics, and business employ functions with many variables. This course extends the basic concepts of single-variable calculus developed in MAT 225 and MAT 275 to functions of several variables. Topics include vectors, the geometry of space, vector-valued functions, motion in space, partial derivatives and multiple integrals.

Differential equations are useful in modeling real-world phenomenon involving rates of change such as the spread of disease, the change in a population, the free fall of an object, and the decay of a radioactive substance. This is a first course in differential equations. Topics include solving first- and higher-order differential equations and modeling with first- and higher-order differential equations.

This is a first course in linear algebra and matrices. Topics include systems of linear equations, linear independence, matrices of linear transformations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors. After mastering the basic concepts and skills, students will use their knowledge of linear algebra to model a selection of applied mathematics problems in business, science, computer science and economics.

Algebra is concerned with sets of objects and operations on these sets. This course will take students beyond the real number and polynomials to groups and other algebraic structures. In a modern, or abstract algebra course, one assumes a small number of basic properties as axioms and then proves many other properties from the axioms. This will assist the student in becoming more proficient at proof-writing.

This course provides a theoretical foundation for single-variable calculus concepts. Topics include the structure of the real numbers, sequences, continuity, differentiation and Riemann integration. This course will be run as a seminar that emphasize problem solving, proof writing and orally defending proofs.