|
|
|
|
|
|
|
Course Criteria
Add courses to your favorites to save, share, and find your best transfer school.
-
4.00 Credits
Lecture, three hours; discussion, two hours. Basic properties of rings; ideals, quotient rings; polynomial and matrix rings. Elements of field theory. Prerequisite: Mathematics 120A.
-
4.00 Credits
Lecture, three hours. Galois Theory: proof of the impossibility of certain ruler-andcompass constructions (squaring the circle, trisecting angles); nonexistence of analogues to the "quadratic formula" for polynomial equations of degree 5 orhigher. Prerequisites: Mathematics 3A or 6G; Mathematics 120A. Previous or concurrent enrollment in Mathematics 120B and 121A recommended. Formerly Mathematics 124.
-
4.00 Credits
Lecture, three hours; discussion, two hours. Introduction to modern abstract linear algebra. Special emphasis on students doing proofs. 121A: Vector spaces, linear independence, bases, dimension. Linear transformations and their matrix representations. Theory of determinants. 121B: Canonical forms; inner products; similarity of matrices. Prerequisite for 121A: Mathematics 3A or 6G.
-
4.00 Credits
Lecture, three hours. Proof of the impossibility of certain ruler-and-compass constructions (squaring the circle; trisecting angles); nonexistence of analogs to the"quadratic formula" for polynomial equations of degree 5 or higher. The necessary algebra introduced as needed. Prerequisites: Mathematics 3A or 6G; Mathematics 120A. Previous or concurrent enrollment in Mathematics 120B and 121A recommended.
-
4.00 Credits
Lecture, three hours; discussion, two hours. The style of precise definition and rigorous proof which is characteristic of modern mathematics. Topics include set theory, equivalence relations, proof by mathematical induction, and number theory. Students construct original proofs to statements. Strongly recommended for freshman and sophomore Mathematics majors as preparation for upper-division courses such as Mathematics 120 and 140. Prerequisite: Mathematics 2A or Mathematics 6D/ICS 6D.
-
4.00 Credits
Lecture, three hours. Introductory course emphasizing applications. 130B: Conditional probability and conditional expectations; Markov chains. 130C: Exponential distribution and Poisson process; Brownian motion; additional topics, such as option pricing, as time permits. Prerequisites: for 130B: Mathematics 2A-B, and either 130A, 131A, 132A, Statistics 120A, or Mathematics 67 and either 6G or 3A; for 130C: Mathematics 130B.
-
3.00 Credits
Lecture, three hours; discussion, one to two hours. Introductory course covering basic principles of probability and statistical inference. 131A: Axiomatic definition of probability, random variables, probability distributions, expectation. 131B: Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference. 131C: Linear regression, analysis of variance, model checking. Prerequisites: for 131A-B: Mathematics 2A-B; 2D and 2J or 4; for 131C: Mathematics 131A-B; 3A or 6G. Same as Statistics 120A-B-C.
-
4.00 Credits
Lecture, three hours. Sample selection, stratification, cluster sampling, double-sampling procedures, optimal allocation, probability-proportional- to-size sampling. Applications to problems in economics, business, public health, agriculture, and the social sciences. Prerequisites: for 132B: Mathematics 2A-B, and either 130A, 131A, 132A, Statistics 120A, or Mathematics 67 and either 6G or 3A; for 132C: Mathematics 132B.
-
4.00 Credits
Lecture, three hours; discussion, two hours. Introduction to real analysis including: the real number system, convergence of sequences, infinite series, differentiation and integration, and sequences of functions. Students are expected to do proofs. Prerequisites: Mathematics 2D, 2J; Mathematics 13 is strongly recommended.
-
4.00 Credits
Lecture, three hours; discussion, two hours. 140C: Rigorous treatment of multivariable differential calculus. Jacobians, Inverse and Implicit Function theorems. Prerequisites: some background in linear algebra (Mathematics 3A, 6G, or 2J), and 140B. 140D: Rigorous treatment of multivariable integral calculus. Multiple integrals in Rn; iterated integrals and Fubini's theorem; change-of-variables theorem; differential forms and Stokes' theorem. Prerequisite: Mathematics 2E and 140C.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Privacy Statement
|
Terms of Use
|
Institutional Membership Information
|
About AcademyOne
Copyright 2006 - 2024 AcademyOne, Inc.
|
|
|