# Math course description

Prerequisites: Mathematics Description: This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing financial instruments, or "derivatives. Abstract Algebra III 4 Third course in a rigorous three-quarter introduction to the methods and basic structures of higher algebra.

### Umass math courses

Gauss and mean curvatures, geodesics, parallel displacement, Gauss-Bonnet theorem. MATH 10B. Precalculus 4 Functions and their graphs. Prior or concurrent enrollment in MATH is highly recommended. Lab activities will include making and using math manipulatives, comparing different problem solving techniques, making interdisciplinary connections, and experiencing math concepts through auditory, visual, and kinesthetic approaches to inquiry-based activities. Partial differentiation. Convex Analysis and Optimization III 4 Convex optimization problems, linear matrix inequalities, second-order cone programming, semidefinite programming, sum of squares of polynomials, positive polynomials, distance geometry. Non-course-based Option. Hamilton-Jacobi theory, initial value problems for hyperbolic and parabolic systems, boundary value problems for elliptic systems.

Pedagogical issues will emerge from the mathematics and be addressed using current research in teaching and learning geometry. Recommended preparation: course work in linear algebra and real analysis.

Prior or concurrent enrollment in MATH is highly recommended. Statistical Methods 4 Introduction to probability.

## Umass math 131

Further Topics in Several Complex Variables 4 Continued development of a topic in several complex variables. Topics include formal and convergent power series, Weierstrass preparation theorem, Cartan-Ruckert theorem, analytic sets, mapping theorems, domains of holomorphy, proper holomorphic mappings, complex manifolds and modifications. Pre-Algebra Credit s : 3 This course provides important skill building in basic computational skills, the language of mathematics, and problem solving required for pre-college level math courses. Inner product spaces and special types of linear operators over real or complex fields : orthogonal, unitary, self-adjoint, hermitian. They explore the concepts of perpendicular and parallel lines and planes. This multimodality course will focus on several topics of study designed to develop conceptual understanding and mathematical relevance: linear relationships; exponents and polynomials; rational expressions and equations; models of quadratic and polynomial functions and radical equations; exponential and logarithmic functions; and geometry and trigonometry. Bisection and related methods for nonlinear equations in one variable. Further Topics in Combinatorial Mathematics 4 Continued development of a topic in combinatorial mathematics.

Topics include set operations, counting techniques and probability, random variables and distribution functions, limits and continuity, derivatives, graphing and optimization, exponential and logarithmic functions, antiderivatives, integration, and applications to management, economics, and business.

Students will be able to apply principles of polynomial and rational equations, functions and their inverses, graphs, systems of equations, complex numbers, sequences, and exponential and logarithmic functions.

Introduction to Partial Differential Equations 4 An introduction to partial differential equations focusing on equations in two variables.

Topics include unique factorization, irrational numbers, residue systems, congruences, primitive roots, reciprocity laws, quadratic forms, arithmetic functions, partitions, Diophantine equations, distribution of primes.

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