Topics include operations with rational numbers and decimals, problem solving, equations of lines, and graphing linear functions. (Math 0015 is a pass - fail course. It does not count towards the number of credits required for graduation.) Topics include algebraic operations, linear and quadratic equations, polynomials, exponentials, systems of linear equations, problem solving, graphing lines, and parabolas. Mathematical concepts and applications for the non-specialist. Selected topics from areas such as Linear Programming, Management Science, Counting Techniques, Probability, and Statistics. Contemporary mathematical applications for the non-specialist. Deals with the general areas of social choice, size, and shape. Specific topics include voting systems, fair division and apportionment, game theory, growth and form, size of populations, measurement, and geometric patterns. This course presents a one-semester overview of the basic topics in calculus, demonstrating their applications in a wide variety of fields. A review of elementary skills will be given during the first week of the semester. This course provides a firm foundation for the study of statistics in other fields. Although no one field is emphasized to the exclusion of others, applications are drawn from psychology, political science, exercise science, and other areas. Bridges the gap in both depth and content between elementary algebra
(Mathematics 0045) and precalculus (Mathematics C074). Topics include
the real number system; operations with algebraic expressions; equations
and inequalities; exponents and radicals; factoring; algebraic, exponential,
and logarithmic functions. A preparatory course for Mathematics C075 and Mathematics C085. Topics include roots of polynomial equations; inequalities; algebraic operations with and graphs of polynomial, rational, exponential and logarithmic functions; triangle trigonometry; analytic trigonometry. Mathematics C075 is an intuitive treatment of calculus with emphasis on applications rather than theory. Topics include: the coordinate plane, functions, limits, continuity, differentiation, applications of differentiation, the definite integral, the Fundamental Theorem of Calculus. Mathematics 0076 is an intuitive treatment of calculus with an emphasis on applications rather than theory. Topics include applications of integration, logarithmic and exponential functions, techniques of integration, improper integrals, L'Hopital' s rule, infinite series. of C or better or its equivalent. Mathematics C085 is an introduction to analytic geometry; functions; limits and continuity; differentiation of algebraic and trigonometric functions; curve sketching, applications; anti-derivatives; the definite integral and the fundamental theorem of calculus. Applications of the definite integral, transcendental functions, properties and applications, techniques of integration, improper integrals, polar coordinates, convergence of sequences and series. Honors section of Mathematics C055. Honors section of Mathematics C065. Honors section of Mathematics C085 - 0086. This course will condense the most important concepts and techniques of differential and integral calculus usually covered in two semesters into one semester. It will be assumed that students in this course already have some facility with techniques of calculus. Consequently, a considerable amount of time will be spent on the concepts of calculus. Upon completing the course students will be able to take Math 0127, Calculus III. Topics include limits and continuity, derivatives and rules of differentiation, derivatives of polynomial, rational, algebraic, trigonometric, exponential, logarithmic and inverse trigonometric functions, the Mean Value Theorem, L’Hospital’s rule, optimization, graphing, the definite integral, the Fundamental Theorem of Calculus, u-substitution and integration by parts, limits of sequences, infinite series, convergence tests, power series, Taylor series. A survey of various mathematical recreations, puzzles, and games. Emphasis on developing problem-solving techniques many of which are applicable in other fields. Mathematics 0117 is an intuitive treatment of Calculus with an emphasis on applications rather than theory. Topics include; vectors in three-dimensional space, vector valued functions, partial derivatives, multiple integrals, and an introduction to vector analysis. Power series, Taylor series, vectors in two or three dimensions, lines and planes in space, parametric equations, vector functions and their derivatives. Functions of several variables, partial derivatives, multiple integrals, line integrals, and Green's Theorem. Sets, relations, functions, logic, ordered fields, induction, cardinality. Note: Mathematics 0127 may be taken concurrently with this course. Only One of the following courses may be credited towards the B.A. degree: Mathematics W141; CIS 0066. Vectors and vector spaces, matrices, determinants, systems of linear equations, linear transformations, inner products, and eigenvalues. In sections with 4 credits there is a required lab, where a computing lab is used to demonstrate topics and provide hands-on experience with the ideas encountered. Activities designed to promote understanding are the primary focus. Sections without the lab must be taken for 3 credits. Honors section of Mathematics W115. Divisibility properties of integers, prime factorization, distribution of primes, linear and quadratic congruences, primitive roots, quadratic residues, quadratic reciprocity, simple Diophantine equations, cryptography. Introduction to the theory of groups, rings, and fields. Mathematical techniques and algorithms which lend themselves to computer implementation and which form a basic repertoire for the mathematician, scientist, or engineer. Extensive computer utilization. The axiomatic definition of probability and its properties, combinatorial analysis, random variables, general properties of continuous random variables, normal and exponential distributions, expected values, Markov chains, Law of Large Numbers, Chebyshev's inequality, and stochastic processes. The emphasis is on the use of probability in solving problems rather than detailed development of the theory. Counting techniques, axiomatic definition of probability, conditional probability, independence of events, Bayes Theorem, random variables, discrete and continuous probability distributions, expected values, moments and moment generating functions, joint probability distributions, functions of random variables, covariance and correlation. Random sampling, sampling distributions, t, chi-squared and F distributions, unbiasedness, minimum variance unbiased estimators, confidence intervals, tests of hypothesis, Neyman-Pearson Lemma, uniformly most powerful tests. The real number system, sequences and their limits, the least upper and the greatest lower bounds, the completeness property, point-set topology of the real numbers, open, closed, compact and connected sets, generalizations to the n-dimensional space, continuous functions, differentiation of functions of one variable, the Mean Value Theorem and its applications. The Riemann integral and the Fundamental Theorem of Calculus, infinite series, convergence tests, power and Taylor series, uniform convergence, operations with power series, partial derivatives, and multiple integrals, transformations of multiple integrals, integrals over curves and surfaces, theorems of Green, Gauss, and Stokes, the divergence theorem. This is a course in ordinary differential equations. Topics include first order o.d.e.’s, linear second order o.d.e.’s, systems of differential equations, numerical methods and the Laplace transform.
Orthogonal polynomials including Legendre and Tchebycheff polynomials, Fourier series, partial differential equations, boundary value problems, the phase plane, stability, Liapunov's method, eigenvalue problems, and introduction to functions of a complex variable. Solution of systems of nonlinear equations, solution of initial value problems, matrix norms and the analysis of iterative solutions, numerical solution of boundary value problems and partial differential equations, and introduction to the finite element method. A study of the properties of projective, affine, Euclidean and non-Euclidean spaces and their transformation groups. Open to juniors and seniors who desire two credits of independent study. Primarily for members of the problem solving group who desire to receive credit for their work. Intensive study in a specific area. May be taken in either semester. The development of the major mathematical concepts from ancient times to the present , emphasizing topics in the standard undergraduate curriculum. Special attention will be paid to the history of mathematics and mathematics education in the United States. Markov chains, exponential distribution, Poisson process, continuous time Markov chains, Brownian motion, stationary processes. Complex numbers, analytic functions, Cauchy's theorem, residues, power series, Laurent series, conformal mappings. The construction and study of mathematical models for physical, economic, and social processes. The solution and properties of first and second order equations; heat and wave equation. Elliptic boundary value problems and Green's functions. Hyperbolic problems and the theory of characteristics-Finite difference methods. The equations of math ematical physics. The theory and applications of various topics, including linear and dynamic programming; game theory; transportation, assignment, and network problems; inventory problems; scheduling and queueing problems. Miscellaneous problems in mathematics and their applications. Possible sources include challenging problems from previous math courses, Math Monthly problems, Putnam exams, and computer applications. Problems will be solved both individually and in groups. (Capstone W course) Topological and metric spaces, continuity, compactness, connectedness, convergence. Introduction to algebraic and combinatorial topology, classification of compact surfaces, fundamental groups. Basic theorems and applications of combinatorial analysis, including generating functions, difference equations, Polya's theory of counting, graph theory, matching, and block diagrams. Open to juniors and seniors who desire two credits of independent study. Primarily for members of the problem solving group who desire to receive credit for their work. |