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Course Criteria
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3.00 Credits
08F: 11 09F: Arrange Number theory is that part of mathematics dealing with the integers and certain natural generalizations. Topics include modular arithmetic, unique factorization into primes, linear Diophantine equations, and Fermat's Little Theorem. Discretionary topics may include cryptography, primality testing, partition functions, multiplicative functions, the law of quadratic reciprocity, historically interesting problems. Prerequisite: Mathematics 8. Dist: QDS. Pomerance.
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3.00 Credits
08F, 09F: 12 A study and analysis of important numerical and computational methods for solving engineering and scientific problems. The course will include methods for solving linear and nonlinear equations, doing polynomial interpolation, evaluating integrals, solving ordinary differential equations, and determining eigenvalues and eigenvectors of matrices. The student will be required to write programs and run them on the computer. Prerequisite: Mathematics 23, and Computer Science 5 or 14. Dist: QDS.
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2.00 Credits
F, W, S: Arrange All students must take a journal club/RIP course during each term of residence, except summer. An essential element of scientific training is in the critical analysis and communication of experimental research in an oral format. Evaluation will be based on quality of the work described, quality of critical analysis, and on presentation style, including effective use of audio-visual materials. All students will be required to participate in at least one Journal Club/Research in Progress series. Although minor variations in format exist among the several series, all students will make oral presentations that describe work from the current literature. Normally these series meet every other week for two hours. This course is not open to undergraduates. M/I 264. Immunology M/I 265. Molecular Pathogenesis M/I 271. Chromatin Structure
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3.00 Credits
09W: 10A 10W: Arrange This course will prepare students to read the technical literature in mathematical biology, epidemiology, pharmacokinetics, ecological modeling and related areas. Topics include systems of nonlinear ordinary differential equations, equilibria and steady state solutions, phase portraits, bifurcation diagrams, and some aspects of stability analysis. Emphasis is placed on the student's ability to analyze phenomena and create mathematical models. This interdisciplinary course is open to mathematics majors, biology majors, and students preparing for a career in medicine. Prerequisite: Mathematics 22. Note: Students without the mathematical prerequisites can take this course as Mathematics 4: no student may take both Mathematics 4 and 27 for credit, and only Mathematics 27 is eligible to count towards the major in mathematics. Dist: QDS. Wallace.
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3.00 Credits
09W: 10 10W: Arrange Beginning with techniques for counting-permutations and combinations, inclusion-exclusion, recursions, and generating functions-the course then takes up graphs and directed graphs and ordered sets, and concludes with some examples of maximum-minimum problems of finite sets. Topics in the course have application in the areas of probability, statistics, and computing.Prerequisite: Mathematics 8, or Mathematics 3 and 6. Dist: QDS. Winkler.
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3.00 Credits
09S: 11 What does it mean for a function to be computable This course examines several different mathematical formalizations of the notion of computability, inspired by widely varying viewpoints, and establishes the surprising result that all these formalizations are equivalent. It goes on to demonstrate the existence of noncomputable sets and functions, and to make connections to undecidable problems in other areas of mathematics. The course concludes with an introduction to relative computability. This is a good companion course to Computer Science 39; the two share only the introduction of Turing machines. Offered in alternate years. Prerequisite: None, but the student must be willing to learn to work abstractly and to read and write proofs. Dist: QDS. Weber.
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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, subsequent 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. Mentor from 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, subsequent 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. Mentor from 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, subsequent 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. Mentor from the Program.
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3.00 Credits
08F: 9L, 11, 12, 09W: 10 09F, 10W: Arrange This course is the basic introduction to calculus. Students planning to specialize in mathematics, computer science, chemistry, physics, or engineering should elect this course in the fall term. Others may elect it in the winter. A study of polynomials and rational functions leads to the introduction of the basic ideas of differential and integral calculus. The course also introduces exponential, logarithmic, and trigonometric functions. The emphasis throughout is on fundamental ideas and problem solving. Mathematics 3 is open to all students who have had intermediate algebra and plane geometry. No knowledge of trigonometry is required. The lectures are supplemented by problem sessions. Dist: QDS. Elizalde, Lahr, Mileti (fall), Arkowitz (winter).
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