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Course Criteria
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4.00 Credits
Lecture, three hours. Introduction to some of the mathematics used in the making and breaking of codes, with applications to classical ciphers and public key systems. The mathematics which is covered includes topics from number theory, probability, and abstract algebra. Prerequisites: Mathematics 2A-B; 3A or 6G.
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4.00 Credits
Topics include: graph types, matching in graphs; Menger's Theorem; Kuratowski's Theorem. Prerequisites:Mathematics 2B and either 3A or 6G.
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4.00 Credits
Topics include: coloring maps, plane graphs, vertices, and edges; Hadwiger's Conjecture; Hamilton Cycles; Ramsey Theory. Prerequisite: Mathematics 174A.
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4.00 Credits
Lecture, three hours. Introduces the mathematics of finance with an emphasis on financial derivatives. After a review of certain tools from probability, statistics, and elementary differential and partial differential equations, concepts such as hedging, arbitrage, Puts, Calls, and the design of portfolios are discussed. Prerequisites: Mathematics 2A-B-J. Same as Economics 135.
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4.00 Credits
Lecture, three hours. The ring of integers. Divisibility. Prime numbers and factorization. Number-theoretic functions such as the Moebius function and the Euler function. Congruences, Moebius inversion, perfect numbers, diophantine equations, quadratic residues. Other topics as time permits. Prerequisite: Mathematics 2J.
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4.00 Credits
Lecture, three hours. Topics vary from year to year. Some possible topics: mathematics in ancient times; the development of modern analysis; the evolution of geometric ideas. Students are assigned individual topics for term papers. Prerequisite: Mathematics 2D, 2J, 3A or 6G, 3D, 120A, 140A. Not offered every year.
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4.00 Credits
Lecture, three hours. Offered from time to time, but not on a regular basis. Content and prerequisites vary with the instructor. May be repeated for credit as topics vary.
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2.00 Credits
Lecture, two hours; fieldwork, two hours. Enrollment limited to upperdivision Mathematics majors participating in the Mathematics for Education specialization, or students in related majors. Admission requires approval of Department Tutor Supervisor. Focus is on historic and current mathematical concepts related to student learning and effective math pedagogy, with fieldwork in grades 6-14. For students not in the specialization in Mathematics for Education, this course satisfies no requirements other than contribution to the 180 units required for graduation. Pass/Not Pass only. Prerequisites: Mathematics 2D; 2J; 3D; 13 or 120A or 140A. May be taken twice for credit.
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2.00 Credits
Lecture, two hours; fieldwork, two hours. Capstone course for the Mathematics Subject-Matter Preparation (SMP) program. Engages students in reviewing and conducting current research on significant issues related to the teaching and learning of mathematics in the secondary classroom. Corequisite: Mathematics 192 recommended. May be taken twice for credit.
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2.00 Credits
Develops ability in analytical thinking and problem solving, using problems of the type found in the Mathematics Olympiad and the Putnam Mathematical Competition. Students taking the course in fall will prepare for and take the Putnam examination in December. Pass/Not Pass only. NOTE: satisfies no requirement other than contribution to the 180 units required for graduation. Recommended for prospective teachers. May be taken twice for credit.
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