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Course Criteria
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3.00 Credits
PQ: MATH 10600, or placement into MATH 13100 or higher. While students may take MATH 11300 without having taken MATH 11200, it is recommended that MATH 11200 be taken first. Either course in this sequence meets the general education requirement in mathematical sciences. These courses are at the level of difficulty of the MATH 13100-13200-13300 calculus sequence. They cover the basic conceptual foundations of mathematics by examining the ideas of number and symmetry. The first quarter addresses number theory, including a study of the rules of arithmetic, integral domains, primes and divisibility, congruences, and modular arithmetic. The second quarter's main topic is symmetry and geometry, including a study of polygons, Euclidean construction, polyhedra, group theory, and topology. The courses emphasize the understanding of ideas and the ability to express them through rigorous mathematical arguments. MATH 11200-11300: Autumn, Winter; MATH 11200: Spring.
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1.00 Credits
PQ: Invitation only based on adequate performance on the mathematics placement test or MATH 10600. Students may not take the first two quarters of this sequence for P/F grading. MATH 13100-13200 meets the general education requirement in mathematical sciences. This sequence provides the opportunity for students who are somewhat deficient in their precalculus preparation to complete the necessary background and cover basic calculus in three quarters. This is achieved through three regular one-hour class meetings and two mandatory one-and-one-half hour tutorial sessions each week. A class is divided into tutorial groups of about eight students each, and these meet with an undergraduate junior tutor for problem solving related to the course. The Autumn Quarter component of this sequence gives a careful treatment of limits and the continuity and differentiability of algebraic functions. Topics examined in the Winter Quarter include applications of differentiation; exponential, logarithmic, and trigonometric functions; the definite integral and the fundamental theorem, and applications of the integral. In the Spring Quarter, subjects include more applications of the definite integral, infinite sequences and series, and Taylor expansions. Students are expected to understand the definitions of key concepts (i.e., limit, derivative, integral) and to be able to apply definitions and theorems to solve problems. In particular, all calculus courses require students to do proofs. Students completing MATH 13100-13200-13300 have a command of calculus equivalent to that obtained in 15100-15200-15300. MATH 13100-13200-13300: Autumn, Winter, Spring; MATH 13100-13200: Winter, Spring.
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3.00 Credits
PQ: Superior performance on the mathematics placement test, or MATH 10600. Students may not take the first two quarters of this sequence for P/F grading. MATH 15100-15200 meets the general education requirement in mathematical sciences. This is the regular calculus sequence in the department. Students entering this sequence are to have mastered appropriate precalculus material and, in many cases, have had some previous experience with calculus in high school or elsewhere. MATH 15100 undertakes a careful treatment of limits, the differentiation of algebraic and transcendental functions, and applications. Work in MATH 15200 is concerned with the mean value theorem, integration, techniques of integration, and applications of the integral. MATH 15300 deals with additional techniques and theoretical considerations of integration, infinite sequences and series, and Taylor expansions. All Autumn Quarter offerings of MATH 15100, 15200, and 15300 begin with a rigorous treatment of limits and limit proofs. MATH 15100-15200-15300: Autumn, Winter, Spring; MATH 15200-15300: Autumn, Winter; MATH 15300: Autumn.
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3.00 Credits
PQ: Invitation only based on superior performance on the calculus placement test. Students may not take the first two quarters of this sequence for P/F grading. MATH 16100-16200 meets the general education requirement in mathematical sciences. MATH 16100-16200-16300 is an honors version of MATH 15100-15200-15300. A student with a strong background in the problem-solving aspects of one-variable calculus may, by suitable achievement on the calculus placement test, be permitted to register for MATH 16100-16200-16300. This sequence emphasizes the theoretical aspects of one-variable analysis and, in particular, the consequences of completeness in the real number system. MATH 16300 also includes an introduction to linear algebra. At least one section of this sequence is offered as an inquiry-based learning (IBL) course. Students interested in IBL should have an AP score of 5 on the BC Calculus exam and fluency in spoken English. Autumn, Winter, Spring.
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3.00 Credits
PQ: MATH 16300 or 19900. This course covers basic properties of the integers following from the division algorithm, primes and their distribution, and congruences. Additional topics include existence of primitive roots, arithmetic functions, quadratic reciprocity, and transcendental numbers. The subject is developed in a leisurely fashion, with many explicit examples. Autumn.
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3.00 Credits
PQ: MATH 16300 or 19900. This course covers advanced topics in geometry, including Euclidean geometry, spherical geometry, and hyperbolic geometry. We emphasize rigorous development from axiomatic systems, including the approach of Hilbert. Additional topics include lattice point geometry, projective geometry, and symmetry. Winter.
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3.00 Credits
PQ: MATH 15300 or equivalent. This course takes a concrete approach to the basic topics of multivariable calculus. Topics include a brief review of one-variable calculus, parametric equations, alternate coordinate systems, vectors and vector functions, partial derivatives, multiple integrals, and Lagrange multipliers. Autumn, Winter, Spring.
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3.00 Credits
PQ: MATH 13300 or 15200. This course takes a concrete approach to the basic topics of linear algebra. Topics include vector geometry, systems of linear equations, vector spaces, matrices and determinants, and eigenvalue problems. Autumn, Winter, Spring.
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3.00 Credits
PQ: Superior performance on the mathematics placement test or MATH 15300 or 13300. Students may not use both MATH 16300 and 19900 to satisfy major or minor requirements. This course is intended for students who are making the transition from MATH 15300 to 20300, or for students who need more preparation in learning to read and write proofs. This course covers the fundamentals of theoretical mathematics and prepares students for upper-level mathematics courses beginning with MATH 20300. Topics include the construction of the real numbers, completeness and the least upper bound property, the topology of the real line, the structure of finite-dimensional vector spaces over the real and complex numbers. Autumn, Winter, Spring.
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3.00 Credits
PQ for MATH 20000: MATH 15300 or 19620 or equivalent. PQ for MATH 20100: MATH 20000, or both 19520 and 19620, or equivalent. This sequence is intended for students who are majoring in a department in the Physical Sciences Collegiate Division other than mathematics. MATH 20000 covers multivariable calculus, including the algebra and geometry of Euclidean space, differentiation and integration of functions of several variables, vector valued functions and the classical theorems of vector analysis (i.e., theorems of Green, Gauss, and Stokes). MATH 20100 introduces ordinary differential equations (e.g., first and second order linear differential equations, series solutions, and the Laplace transform) and complex analysis (i.e., basic properties of the complex plane and analytic functions through Cauchy's theorem). Autumn, Winter; Winter, Spring.
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