The department offers minors in Actuarial Mathematics and Pure Mathematics, both of which can be used to enhance the career options for students who choose to major in another discipline. Math skills are valuable for careers in economics, finance, statistics, insurance, and teaching.
Permission of Instructor
4.00
This course provides an alternative to MATH 165 (Calculus I) for those students who have taken MATH 134 (Calculus for Management and Social Sciences) but who do not have the trigonometric precalculus prerequisite (such as MATH 121) for MATH 165. In other words, the sequence MATH 134 / MATH 164 serves as an alternative to the sequence MATH 121 / MATH 165, and similarly prepares students to take MATH 166 (Calculus II). The course includes a thorough review of trigonometry and other precalculus topics. Aspects of limits and differentiation which students have already seen in MATH 134 are presented briefly, but in most cases with more emphasis on conceptual understanding, and often illustrated using more complicated examples. New calculus topics (i.e. not covered in MATH 134) include one-sided limits, special trigonometric limits, differentiability, derivatives of trigonometric functions and their inverses, derivatives of general inverse functions, logarithmic and implicit differentiation, related rates, L'Hopital's rule, intermediate values theorem, Rolle's theorem, mean values theorem, Newton's method, and linearization. 4 lecture hours plus 1 recitation session each week. Normally offered in fall.
MATH-121 with a minimum grade of C, MATH-075, or MATH level 5
4.00
Functions, limits and continuity, squeeze theorem, limits at infinity; instantaneous rate of change, tangent slopes, and the definition of the derivative of a function; power, product, and quotient rules, trig derivatives, chain rule, implicit differentiation; higher order derivatives; derivatives of other transcendental functions (inverse trig functions, exponential and log functions, hyperbolic trig functions); applications of the derivative (implicit differentiation, related rates, optimization, differentials, curve sketching, L'Hopital's rule); anti-derivatives; indefinite integrals; Fundamental Theorem; applications (net change). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.
MATH-164 or MATH-165 with a minimum grade of C
4.00
Riemann sums and definite integrals; Fundamental Theorem; applications (areas); integration of exponential functions, trig functions, and inverse trig functions; techniques of integration (substitution, by parts, trig integrals, trig substitution, partial fractions); area, volume, and average value applications; differential equations (separable, exponential growth, linear); improper integrals; infinite sequences and series; convergence tests; power series; Taylor and Maclaurin series (computation, convergence, error estimates, differentiation and integration of Taylor series). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.
Take MATH-121, MATH-164, MATH-165, or MATH-166
4.00
Topics covered include: Logic and set theory, basic techniques of proof, relations and functions and their properties (equivalence relations, partial order relations, recurrence relations and their solutions), cardinality, elementary number theory, mathematical induction, counting, Pigeonhole principle, discrete probability. Normally taken second semester freshman year.
MATH 166 with grade of C or better
4.00
Parametric equations and polar coordinates (curves, areas, conic sections); vectors and the geometry of space (the dot product, vector arithmetic, lines and planes in 3-space, the cross product, cylinders and quadratic surfaces); vector functions (limits, derivatives and integrals, motion in space); partial derivatives (functions of several variables, limits and continuity, tangent planes and differentials, chain rule, directional derivatives, gradient, extrema, Lagrange multipliers); multiple integrals (double integrals, applications); vector calculus (vector fields, line integrals, fundamental theorem for line integrals, Green's Theorem, curl and divergence, parametric surfaces, surface integrals). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.
Take MATH-185 with a grade of C or better
4.00
this course is intended to provide a firm foundation for and a taste of the study of advanced mathematics. While the course content varies somewhat, it is designed to give students a deeper understanding of the algebraic and analytical structure of the integers, the rational numbers and the real numbers and how they act as a building block to a variety of fields of mathematics. Students are introduced to the process of mathematical discovery and the language of mathematics. Exercises and projects are designed to illustrate the need for proof and to further refine the student's ability to analyze, conjecture and write mathematical proofs. This course is a prerequisite for most upper level mathematics courses and, after completing it a student will be in a position to determine realistically if he or she ought to major or minor in mathematics.
Residency Requirement Policy: In the College of Arts and Sciences, a two-course (8 credit) residency requirement must be satisfied for completion of a minor and a four-course (16 credit) residency requirement must be satisfied for the completion of a major.
Minor Programs Policy: A student declaring a minor may use no more than two courses from a major to fulfill the requirements for the minor. No more than one course from one minor may count toward the fulfillment of a second minor. Students may not minor in a subject in which they are also completing a major. For more information, see the Minor Programs section of the CAS Degree Requirements page.
Permission of Instructor
4.00
This course provides an alternative to MATH 165 (Calculus I) for those students who have taken MATH 134 (Calculus for Management and Social Sciences) but who do not have the trigonometric precalculus prerequisite (such as MATH 121) for MATH 165. In other words, the sequence MATH 134 / MATH 164 serves as an alternative to the sequence MATH 121 / MATH 165, and similarly prepares students to take MATH 166 (Calculus II). The course includes a thorough review of trigonometry and other precalculus topics. Aspects of limits and differentiation which students have already seen in MATH 134 are presented briefly, but in most cases with more emphasis on conceptual understanding, and often illustrated using more complicated examples. New calculus topics (i.e. not covered in MATH 134) include one-sided limits, special trigonometric limits, differentiability, derivatives of trigonometric functions and their inverses, derivatives of general inverse functions, logarithmic and implicit differentiation, related rates, L'Hopital's rule, intermediate values theorem, Rolle's theorem, mean values theorem, Newton's method, and linearization. 4 lecture hours plus 1 recitation session each week. Normally offered in fall.
MATH-121 with a minimum grade of C, MATH-075, or MATH level 5
4.00
Functions, limits and continuity, squeeze theorem, limits at infinity; instantaneous rate of change, tangent slopes, and the definition of the derivative of a function; power, product, and quotient rules, trig derivatives, chain rule, implicit differentiation; higher order derivatives; derivatives of other transcendental functions (inverse trig functions, exponential and log functions, hyperbolic trig functions); applications of the derivative (implicit differentiation, related rates, optimization, differentials, curve sketching, L'Hopital's rule); anti-derivatives; indefinite integrals; Fundamental Theorem; applications (net change). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.
Non CAS majors need to have completed at least 15 credits.
3.00
This course introduces students to foundational principles of microeconomic theory, with an emphasis on applications of concepts to management decision-making in specific industry and market settings. It describes and analyzes the interaction of supply and demand and the behavior of the prices of goods, services. It explains the determinations of costs, output, strategic pricing, and governance by firms under conditions of perfect and imperfect competition in a global economy. In addition, it describes the supply demand for factors of production and the impact of taxes and government regulation and intervention on firms and consumers.
Non-CAS majors need to have completed at least 15 credits
3.00
This course examines the workings of the national and the global economy. It will describe the determination of Gross Domestic Product, the problems of unemployment, inflation, and the determination of economic growth. It will also describe and analyze the determination of the country's exchange rate, the balance of payments, and international borrowing and lending. A particular focus will be on understanding economic fluctuations (booms, busts, and recessions) in the domestic economy and its effects on other economies. It will analyze the role of the government and the effects of government spending and taxation on the economy. Furthermore, it will describe and analyze the determination of the quantity of money and interest rates in the economy and the role of the country's central bank. It examines the basis and pattern of international trade and the effects of a country's trade policy on the economy.
MATH-164 or MATH-165 with a minimum grade of C
4.00
Riemann sums and definite integrals; Fundamental Theorem; applications (areas); integration of exponential functions, trig functions, and inverse trig functions; techniques of integration (substitution, by parts, trig integrals, trig substitution, partial fractions); area, volume, and average value applications; differential equations (separable, exponential growth, linear); improper integrals; infinite sequences and series; convergence tests; power series; Taylor and Maclaurin series (computation, convergence, error estimates, differentiation and integration of Taylor series). 4 lecture hours plus 1 recitation session each week. Normally offered each semester.
MATH-165 or MATH-164 with a grade of C or better
4.00
Topics include: random variable and distribution; expectation and variance; special discrete/continuous distributions (uniform, binomial, negative binomial, geometric, hypergeometric, Poisson, normal, and exponential distributions); joint distribution, marginal distribution and conditional distribution; covariance; limit theorems (law of large numbers and central limit theorem); introduction to confidence interval and hypothesis testing; regression analysis. Offered as needed.
MATH-166, 164 or 165 with a minimum grade of C
4.00
This course is mainly designed for students who are interested in financial mathematics and/or actuarial sciences, especially if they plan to take the second actuarial exam, and/or if they plan to study more in financial mathematics. The materials covered include time value of money, annuities, loans, bonds, cash flows and portfolios, general derivatives, options, hedging and investment strategies, forwards and futures, and swaps.
MATH-255 with a minimum C grade
4.00
Calculus based introduction to statistical analysis. Topics include sampling distribution, point estimation, interval estimation, hypothesis testing, regression and correlation analysis.
Residency Requirement Policy: In the College of Arts and Sciences, a two-course (8 credit) residency requirement must be satisfied for completion of a minor and a four-course (16 credit) residency requirement must be satisfied for the completion of a major.
Minor Programs Policy: A student declaring a minor may use no more than two courses from a major to fulfill the requirements for the minor. No more than one course from one minor may count toward the fulfillment of a second minor. Students may not minor in a subject in which they are also completing a major. For more information, see the Minor Programs section of the CAS Degree Requirements page.