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Course Criteria
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3.00 Credits
09W: 11 10W: Arrange Gives prospective Mathematics majors an early opportunity to delve into topics outside the standard calculus sequence. Specific topics will vary from term to term, according to the interests and expertise of the instructor. Designed to be accessible to bright and curious students who have mastered BC Calculus, or its equivalent. This course counts toward the Mathematics major, and is open to all students, but enrollment may be limited, with preference given to first-year students. Prerequisite: Mathematics 8, or placement into Mathematics 11. Dist: QDS. Trout.
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3.00 Credits
08F: 12 09W: 10 09F, 10W: Arrange This course integrates discrete mathematics with algorithms and data structures, using computer science applications to motivate the mathematics. It covers logic and proof techniques, induction, set theory, counting, asymptotics, discrete probability, graphs, and trees. Mathematics 19 is identical to Computer Science 19 and may substitute for it in any requirement. Prerequisite: Computer Science 5, Engineering Sciences 20, or advanced placement. Dist: QDS. Pomerance (fall), Zomorodian (winter).
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3.00 Credits
All terms: Arrange An original individual experimental or theoretical investigation beyond the undergraduate level in Microbiology and Immunology. This course is open only to graduate students, prior to passing their qualifying exam; it may be elected for credit more than once. This course carries one course credit and should be elected by students conducting research and also electing two or more other graduate or undergraduate courses. Staff of the Program.
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3.00 Credits
All terms: Arrange An original individual experimental or theoretical investigation beyond the undergraduate level in Microbiology and Immunology. This course is open only to graduate students, prior to passing their qualifying exam; it may be elected for credit more than once. This course carries two course credits and should be elected by students electing only departmental colloquia in addition to research. Staff of the Program.
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3.00 Credits
All terms: Arrange An original individual experimental or theoretical investigation beyond the undergraduate level in Microbiology and Immunology. This course is open only to graduate students, prior to passing their qualifying exam; it may be elected for credit more than once. This course carries three course credits and should be elected by students conducting research exclusively in any one term. Staff of the Program.
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3.00 Credits
09W: 9L, 11 10W: Arrange Mathematics 1-2 is a two-term sequence. Its purpose is to cover the calculus of Mathematics 3, the standard introduction to calculus, and, at the same time, to develop proficiency in algebra. The sequence is specifically designed for first-year students whose manipulative skill with the techniques of secondary-school algebra is inadequate for Mathematics 3. The objective is to introduce and develop algebraic techniques as they are needed to study the ideas of calculus. The techniques will be taught in class, and the students will be required to practice by solving many drill problems for homework. There will be tutorial-help sessions. Mathematics 1 will include the concepts of function and graph and the basic ideas and applications of differential and integral calculus, at least as they pertain to polynomial functions. In the second course, Mathematics 2, the study of calculus will be continued so that by the end of the sequence the students will have been introduced to the algebra and calculus of the exponential and logarithm functions and the trigonometric functions and to differential equations. Prerequisite: Mathematics 1, or permission of the Department. Dist: QDS. The staff.
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3.00 Credits
08F: 2 09S: 9L 09X, 09F: Arrange Basic concepts of probability are introduced in terms of finite probability spaces and stochastic processes having a finite number of outcomes on each experiment. The basic theory is first illustrated in terms of simple models such as coin tossing, random walks, and casino games. Also included are Markov chain models and their applications in the social and physical sciences. The computer will be used to suggest and motivate theoretical results and to study applications in some depth. There is an honors version of this course: see Mathematics 60. Prerequisite: Mathematics 8. Dist: QDS. The staff (fall), Mileti (spring).
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3.00 Credits
08F: 2 09S: 10 09X, 09F, 10S: Arrange This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing. Students who plan to take either Mathematics 63 or Mathematics 71 are strongly encouraged to take Mathematics 24. Prerequisite: Mathematics 8. Dist: QDS. Rockmore (fall), Luca (spring).
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3.00 Credits
08F, 09W: 10 09S: 10A, 12 09F, 10W, 10S: Arrange This course is a survey of important types of differential equations, both linear and nonlinear. Topics include the study of systems of ordinary differential equations using eigenvectors and eigenvalues, numerical solutions of first and second order equations and of systems, and the solution of elementary partial differential equations using Fourier series. Prerequisite: Mathematics 13. Dist: QDS. Sadykov (fall), Wallace (winter), Sadykov, Chernov (spring).
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3.00 Credits
09W: 12 09S: 10 10W, 10S: Arrange This course is an introduction to the fundamental concepts of linear algebra in abstract vector spaces. The topics and goals of this course are similar to those of Mathematics 22, but with an additional emphasis on mathematical abstraction and theory. (Mathematics 24 can be substituted for Mathematics 22 as a prerequisite for any course or program.) Dist: QDS. Sadykov (winter), Mainkar (spring).
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