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  • MATH 220: Probability and Elementary Statistics

    3.00 Credits
    Wellesley College

    Munson This course is about the mathematics of uncertainty, where we use the ideas of probability to describe patterns in chance phenomena. Probability is the basis of statistics and game theory, and is immensely useful in many fields including business, social and physical sciences, and medicine. The first part of the course focuses on probability theory (random variables, conditional probability, probability distributions), using integration and infinite series. The second part discusses topics from statistics (sampling, estimation, confidence inter-val, hypothesis testing). Applications are taken from areas such as medical diagnosis, quality control, gambling, political polls, and others. Prerequisite: 205. Open to students with a strong background in single-variable calculus (116, 120, or the equivalent) by permission of the instructor Distribution: Mathematical Modeling. Fulfills the Quantitative Reasoning overlay course requirement. Semester: Spring Unit: 1.0
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  • MATH 223: Number Theory

    3.00 Credits
    Wellesley College

    Trenk Number theory is the study of the most basic mathematical objects: the natural numbers (1, 2, 3, etc.). It begins by investigating simple patterns: for instance, which numbers can be written as sums of two squares Do the primes go on forever How can we be sure The patterns and structures that emerge from studying the properties of numbers are so elegant, complex, and important that number theory has been called ?the Queen of Mathematics?. Once studied only for its intrinsic beauty, number theory has practical applications in crypto-graphy and computer science. Topics include the Euclidean algorithm, modular arithmetic, Fermat's and Euler's Theorems, public-key cryptography, quadratic reciprocityMATH 223 has a focus on learning to understand and write mathematical proofs; it can serve as valu-able preparation for 305. Majors can fulfill the major presentation requirement in this course in 2009-10. Prerequisite: 116, 120 or the equivalent; or CS 230 together with permission of the instructor Distribution: Mathematical Modeling Semester: Spring Unit: 1.0
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  • MATH 225: Combinatorics and Graph Theory

    3.00 Credits
    Wellesley College

    Hirschhorn, Trenk Combinatorics is the art of counting possibilities: for instance, how many different ways are there to distribute 20 apples to 10 kids Graph theory is the study of connected networks of objects. Both have important applications to many areas of mathematics and computer science. The course will be taught emphasizing creative problem-solving as well as methods of proof, such as proof by contradiction and induction. Topics include: selections and arrangements, generating functions, recurrence relations, graph coloring, Hamiltonian and Eule-rian circuits, and trees. Prerequisite: 116, 120, or the equivalent; or CS 230 together with permission of the instructor Distribution: Mathematical Modeling Semester: Fall, Spring Unit: 1.0
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  • MATH 251: Topics in Applied Mathematics

    3.00 Credits
    Wellesley College

    NOT OFFERED IN 2009-10. Prerequisite: None Distribution: Mathematical Modeling Semester: N/O Unit: 1.0
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  • MATH 302: Elements of Analysis I

    3.00 Credits
    Wellesley College

    Chang, Sontag Real analysis is the study of the rigorous theory of the real numbers, Euclidean space, and calculus. The goal is to thoroughly understand the familiar concepts of continuity, limits and sequences. We also study metric spaces, which generalize the familiar notion of distance to a broader setting. Topics include metric spaces; compact, complete, and connected spaces; continuous functions; differentiation and inte-gration; limits and sequences; and interchange of limit operations as time permits. Prerequisite: 205 and 206 Distribution: Mathematical Modeling Semester: Fall, Spring Unit: 1.0
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  • MATH 303: Elements of Analysis II

    3.00 Credits
    Wellesley College

    Chang A continuation of MATH 302. Topics chosen from the theory of Riemann integration, measure theory, Lebesgue integration, Fourier series, and calculus on manifolds. Offered in alternate years. Prerequisite: 302 Distribution: Mathematical Modeling Semester: Spring Unit: 1.0
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  • MATH 305: Abstract Algebra

    3.00 Credits
    Wellesley College

    Trenk. Munson In this course, students examine the structural similarities between familiar mathematical objects such as number systems, matrix sets, function spaces, general vector spaces and mod n arithmetic. Topics include groups, rings, fields, homomorphisms, normal subgroups, quotient spaces, isomorphism theorems, divisibility and factorization. Many concepts generalize number theoretic-notions such as Fer-mat's little theorem and the Euclidean algorithm. Optional subjects include group actions and applications to combinatorics. Prerequisite: 206 Distribution: Mathematical Modeling Semester: Fall, Spring Unit: 1.0
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  • MATH 306: Topics in Abstract Algebra

    3.00 Credits
    Wellesley College

    Diesl Topic for 2009-10: Modern Number Theory. This course offers an advanced treatment of number theory from an abstract algebraic point of view. Subjects covered will include unique factorization, congruence, quadratic and cubic reciprocity, Gauss and Jacobi sums, equations over finite fields, and the zeta function. Students who have taken 306 in Spring 2007 or 2008 may repeat this course for credit. Majors can fulfill the presentation requirement in this course in 2009-10. Prerequisite: 305 Distribution: Mathematical Modeling Semester: Spring Unit: 1.0
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  • MATH 307: Topology

    3.00 Credits
    Wellesley College

    NOT OFFERED IN 2009-10. This course covers some basic notions of point-set topology, such as topological spaces, metric spaces, connectedness and compactness, Heine-Borel Theorem, quotient spaces, topological groups, groups acting on spaces, homotopy equiva-lences, separation axioms, Euler characteristic and classification of surfaces. Additional topics include the study of the fundamental group (time permitting). Prerequisite: 302 and 305 Distribution: Mathematical Modeling Semester: N/O Unit: 1.0
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  • MATH 309: Foundations of Mathematics

    3.00 Credits
    Wellesley College

    Sontag This course will introduce students to aspects of set theory and formal logic. The notion of set is one of the fundamental notions of modern mathematics. In fact, other mathematical notions, such as function, relation, number, etc., can be represented in terms of purely set theo-retical notions and their basic properties can be proved using purely set theoretic axioms The course will include the Zermelo-Fraenkel axioms for set theory, the Axiom of Choice, transfinite arithmetic, Zorn's Lemma, ordinal numbers and cardinal numbers. We also study G del's incompleteness theorem, which asserts that any consistent system containing arithmetic has questions that cannot be answered within the system . Offered in alternate years . Prerequisite: 302 or 305; or at least two from 206, 214, 223, 225 Distribution: Mathematical Modeling Semester: Fall Unit: 1.0
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