Students should not consider themselves adequately prepared for
a mathematics course unless they have earned grades of C
or better in all prerequisite courses.
The advice is broken down into the following sections:
MATH 1101 (Mathematical Modeling): This course satisfies the Core A Mathematics requirement for students who will not continue to Precalculus and Calculus. Students will learn several ways to use mathematics to describe and explore real-world data and phenomena.
WARNING: MATH 1101 will not prepare
you for Precalculus, nor will it count in Core Area A if you are
(or become) a Science major. If you think there is a chance you
will be a Science major, you should take MATH 1113 instead.
MATH 1113 (Precalculus): This course is not intended to be a terminal mathematics course; it prepares students for the mainstream calculus courses. Exemption of or credit for MATH 1113 is required of students in the Business School and science majors in A & S. Topics covered include identities, graphs, and word problems involving exponential, logarithmic and trigonometric functions.
MATH 1060 (Mathematics of Decision Making): This course attempts to convey the flavor and variety of mathematics rather than develop skills to be used in later courses. It is usually taken by liberal arts majors. Occasionally, students who are considering majoring in mathematics use this course to get an overview of the subject.
All of these courses require knowledge of MATH 1113.
MATH 2200 is a terminal one-semester
course. Students intending
to major in engineering, a mathematical science, or a physical
science, or who plan to take MATH 2500, should take MATH 2250-2260.
MATH 2200 (Analytic Geometry and Calculus): MATH 2200 is required by the Business School and either MATH 2200 or MATH 2250 is required for all Bachelor of Science Degrees in the college of Arts and Sciences (see note below).
MATH 2200 concentrates on differential calculus of functions of one variable. Topics covered include the definition of derivative in terms of limits, and techniques for computing derivatives of rational, trigonometric, and exponential functions. Applications of the derivative to graphing and word problems involving maximization/minimization and related rates are also emphasized. The class concludes with a discussion of antidifferentiation and applications to science and business.
An A student in
MATH 2200 who realizes he or she wants to continue studying calculus
in MATH 2260 can consult the syllabus and do a bit of preparatory work (Note
the material on the integral in Chapter 5). Please contact the
Associate
Head for permission
to enroll in the class.
If you plan to major in engineering, physics or physics/astronomy, chemistry, geology, physical geography (meteorology), mathematics, computer science, statistics, biochemistry, (microbiology), ecology, genetics, mathematics or science education, economics with a view towards graduate school, or think you might want (have) to take more than one semester of calculus, you should register for MATH 2250, MATH 2300H, or MATH 2400(H). (These courses will also fulfill the MATH 2200 requirement.) If you have further questions, contact your academic adviser.
MATH 2250-2260 (Calculus for Science and Engineering): These are 4-hour courses with no lab. MATH 2250 covers differential calculus and the beginning of integral calculus (approximately the material covered in an advanced-placement high school course, but with more emphasis on word problems), including the Fundamental Theorem of Calculus and some methods of integration. MATH 2260 covers the applications of integral calculus, some material on series and Taylor series, and vector algebra (dot products, cross products and applications).
MATH 2300H-2310H (Honors Calculus): This is the Honors equivalent of MATH 2250-2260.
MATH 2500 (Multivariable Calculus): The continuation of MATH 2260 and MATH 2310H to functions of several variables. (Students who have transfer credit for MATH 2210 should do a quick study of vectors and vector geometry before starting MATH 2500.)
MATH 2500 treats functions of several variables.
The course begins with a review of vector algebra and geometry.
Calculus of functions of several variables is treated: partial
derivatives, directional derivatives, max/min problems in several
variables, multiple integrals, and their physical applications
are discussed. Finally, line integrals, surface integrals, and
the higher dimensional versions of the Fundamental Theorem of
Calculus are discussed.
MATH 2110 (Calculus for Economics): This course is a sequel to MATH 2200 designed for economics majors. Before enrolling in this course, students should be sure it meets requirements in their colleges or degree programs.
Topics in MATH 2110 include the definite integral and its relation
to antiderivatives, partial derivatives and maximization of functions
of several variables including the Lagrange multiplier method,
and an introduction to matrices and linear algebra. Applications
include consumer's and producer's surplus, lines of regression,
and input-output analysis.
MATH 2400(H)-2410(H) (Calculus with Theory): This is the department's most rigorous and extensive calculus sequence. Enrollment is not limited to math majors, but students should be highly motivated and interested in the whys of mathematics, not just the hows. The courses stress the theoretical foundations of calculus (hence having more of a theorem/proof format than the conventional high school or college calculus course) and also include deeper applications to physics. N.B. Credit is allowed for both MATH 2250 (e.g., AP credit) and MATH 2400(H). Many, but not all, of the students in this sequence have AP credit for calculus. Indeed, some of the most successful students in this course over the years have been students who have never had prior experience with calculus.
Students who earn a 5
on
the AP Calculus BC examination will receive 4 hours of credit for MATH
2260 once they complete MATH 2500, MATH 3000, or MATH 3500(H) with a
grade of C or better. Students who are interested in a challenging
mathematics experience should take MATH 3500(H)–3510(H). Those who wish
to truly understand single-variable calculus (why do the Intermediate
Value Theorem and Maximum Value Theorem really work?) and get a deep
foundation in sequences and series material and their applications
should take MATH 2400(H)–2410(H), although to do so one must forgo the
AP credit for MATH 2260.
Well, MATH 2500 (or MATH 3500(H)), of course. The following courses are independent of one another and may be taken any time after MATH 2260 or MATH 2310H. You should try to complete these courses by the end of your sophomore year if you are planning to major in Mathematics. We encourage students considering majoring in mathematics to take a 3000-level course as soon as possible after completing their Calculus II course, so as to be exposed to the proof flavor of mathematics. Most students should take MATH 3200 concurrently with MATH 2500 or MATH 3000. MATH 3200 is the most basic of the 3000-level courses (despite its higher number).
MATH 2700 (Elementary Differential Equations): This course is fairly computational and similar to MATH 2260 or MATH 2210: learning methods of solving differential equations is like learning and organizing integration techniques. Physical and biological applications covered in this course make it important for many science majors.
MATH 3000 (Introduction to Linear Algebra): This course has both computational and theoretical components. It is required of many science majors, and Mathematics Education majors. Topics include systems of linear equations and matrix operations; vector space concepts of independence, spanning, basis, and dimension; dot products and projections; eigenvalues and diagonalization of matrices; and linear transformations. Applications include Markov processes (e.g. forecasting population distributions), finding best linear approximations to given data, and rotations of conic sections into standard position.
MATH 3100 (Sequences and Series): This course also has both theoretical and computational aspects. Concepts of limit and convergence are carefully defined and an arsenal of convergence tests is developed. Taylor's Theorem, a powerful generalization of the mean value theorem, provides an effective way to estimate values of trigonometric and exponential functions to any degree of accuracy. The material in this course is needed in the study of probability and statistics. Students who've taken MATH 2260 will see some overlap in material, but far greater emphasis is placed on proofs in this course. (Ordinarily, students with credit for MATH 2410H should not take this course.)
MATH 3200 (Introduction to Higher Mathematics): This course introduces students to the logical structure of mathematics and gives them experience in writing simple proofs. It should be taken before attempting 4000-level mathematics courses.
MATH 3500(H)-3510(H) (Multivariable Mathematics): This sequence is a more integrated and more conceptual treatment of the material in MATH 2500 and MATH 3000. It highlights the deep connections between linear algebra and multivariable calculus, with greater emphasis on concepts and proofs than 2500–3000. These courses are particularly suited to students who have completed MATH 2410(H) (or who have earned a 5 on the AP Calculus BC test). But they may also be taken by students completing MATH 2260 or MATH 2310H who are ready for a more rigorous and conceptual treatment of mathematics. (Such students may wish to take MATH 3200 concurrently with MATH 3500(H).)
During your freshman and sophomore years you should:
Read Majoring in Mathematics for more
detailed information.