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Calculus Foundations

Introduction to limits and derivatives as preparation for further courses in calculus. Fundamental functions (polynomials, rational functions, exponential, logarithmic, trigonometric) and their graphs will be also reviewed. Other topics include tangent and normal lines, linearization, computing area and rates of change. The emphasis will be on learning to think independently and creatively in the mathematical setting.

Survey of Calculus

One semester survey of the major concepts and computational techniques of calculus including limits, derivatives and integrals. Emphasis on basic examples and applications of calculus including approximation, differential equations, rates of change and error estimation for students who will take no further calculus. Prerequisites: MAT100 or equivalent. Restrictions: Cannot receive course credit for both MAT103 and MAT102. Provides adequate preparation for MAT175. Three classes.

Calculus I

First semester of calculus. Topics include limits, continuity, the derivative, basic differentiation formulas and applications (curve-sketching, optimization, related rates), definite and indefinite integrals, the fundamental theorem of calculus. Prerequisite: MAT100 or equivalent.

Calculus II

Continuation of MAT103. Topics include techniques of integration, arclength, area, volume, convergence of series and improper integrals, L'Hopital's rule, power series and Taylor's theorem, introduction to differential equations and complex numbers. Prerequisite: MAT103 or equivalent.

Mathematics for Economics/Life Sciences

Survey of topics from multivariable calculus as preparation for future course work in economics or life sciences. Topics include basic techniques of integration, average value, vectors, partial derivatives, gradient, optimization of multivariable functions, and constrained optimization with Lagrange multipliers. Students preparing for math track econometrics and finance courses need MAT201/202 instead. Students who complete 175 can continue in 202 if they wish.

Number, Shape and Symmetry

Mathematics is both art and science, and many of its greatest discoveries are generated as much by considerations of abstract beauty as they are by cold logic and utilitarian concerns. This highly interactive, discovery-based course explores some of the intriguing ideas of elementary number theory, including the mathematics of rhythm, number patterns and sequences, counting and probability, mathematical proof and modular arithmetic. Emphasis will be placed on the development of mathematical literacy.

The Magic of Numbers

This course will explore some of the intriguing and beautiful mathematics that underlie the arts, technology, and everyday life. This interactive course will cover materials ranging from prime numbers and encryption codes to Escher drawings, musical rhythms, games of chance, and mathematical designs in nature. Emphasis will be placed on discovering and analyzing patterns in a variety of contexts.

Introduction to Mathematical Thinking

This course begins with general discussion of the nature of mathematics, adopting a broadly historical approach. The aim will be to investigate several important areas of contemporary mathematics. The choice of topic will depend in part on the interests of the class, as determined by a student questionnaire completed during the first class meeting.

Useful Fictions: How and Why Mathematics is Developed and Then Changes the World

Provides a view of mathematics as a living, creative endeavor that classifies as both a science and art, giving a feeling for, and some mastery of, the mathematical way of thinking and an awareness of some of the many applications of mathematics. Starting from a broadly historical approach we will move to investigate several important areas of contemporary mathematics.

Multivariable Calculus

Vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields, and Stokes's theorem. Prerequisite: 104 or equivalent.

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