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100 level | 200 level | 300 level | 400 level | Graduate courses
Math
305/605
Real Analysis I (3)
Prerequisite: Math 221. Introduction to analysis. Real
numbers, limits, continuity, uniform continuity, sequences and series,
compactness, convergence, Riemann integration. An in-depth treatment of
the concepts underlying calculus.
Math 307 Introduction to Probability (3)
Prerequisite: Math 221 or equivalent. An introduction to probability theory. Counting methods, conditional probability and independence. Discrete and continuous distributions, expected value, joint distributions and limit theorems. Prepares student for future work in probability and statistics.
Math 308 Introduction to Statistical Inference (3)
Prerequisite: Math 221, Math 307. Basics of Statistical inference. Sampling distributions, parameter estimation, hypothesis testing, optimal estimates and tests. Maximum likelihood estimates and likelihood ratio tests. Data summary methods, categorical data analysis. Analysis of variance and introduction to linear regression.
Math
309/609
Linear Algebra (4)
Prerequisite: Math 221. An introduction to linear
algebra emphasizing matrices and their applications. Gaussian
elimination, determinants, vector spaces and linear transformations,
orthogonality and projections, eigenvector problems, diagonalizability,
Spectral Theorem, quadratic forms, applications. MATLAB is used as a
computational tool.
Math
311/611
Abstract Algebra I (3)
Prerequisite: Math 221. An introduction to abstract
algebra. Elementary number theory and congruences. Basic group theory:
groups, subgroups, normality, quotient groups, permutation groups. Ring
theory: polynomial rings, unique factorization domains, elementary
ideal theory. Introduction to field theory.
Math 314 Experimental Mathematics(3)
Prerequisites: The class will be made available to any student that has completed the Calculus sequence: Math121,122, 221. The exploration of Mathematical tools in Symbolic Languages. Examples are taken from Calculus, Differential Equations and Linear Algebra.
Math 320 Combinatorics (3)
Prerequisites: Math 121, 122, and either 221 or 309 or
approval of instructor. Basics of combinatorics with emphasis on
problem solving. Provability, pigeonhole principle, Mathematical
induction. Counting techniques, generating functions, recurrence
relations, Polya’s counting formula, a theorem of Ramsey.
Math 325 Theory of Computation(3)
Prerequisites: Math 217 or equivalent. Introduction to the theory of computation: Formal languages, finite automata and regular languages, deterministic and nondeterministic computation, context-free grammars, languages, and pushdown automata. Turing machines, undecidable problems, recursion theorem, computational complexity, NP-completeness..
Math 326 Algorithms and Complexity (3)
Prerequisites: Math 305 or Math 311 or Math 320. Also, students who have taken neither Math 217 or Math 320 should talk with the instructor before registering for the course. A study of important algorithms (including searching and sorting, graph/network algorithms, and algorithms in number theory) and algorithm design techniques (including greedy, recursive, and probabilistic algorithms). Covers the analysis of algorithms (including worst- and average-case analysis) and discussion of complexity classes for decision and enumeration problems (including P, NP, #P, PSPACE).
Math 331/631 Scientific Computing (3)
Prerequisites: Math 221, 224, and Computer Science 101 or equivalent. Errors. Curve fitting and function approximation, least squares approximation, orthogonal polynomials, trigonometric polynomial approximation. Direct methods for linear equations. Iterative methods for nonlinear equations and systems of nonlinear equations. Interpolation by polynomials and piecewise polynomials. Numerical integration. Single-step and multi-step methods for initial-value problems for ordinary differential equations, variable step size. Current algorithms and software.
Math
365
Number Theory and Applications (3)
The subject of number theory is one of the oldest in Mathematics. The
course will cover some basic material and describe interesting
applications. One of the recurrent themes is the realization that
Mathematics that was developed usually for its own sake, has found
applications in many unexpected problems. Some of the topics covered in
the class are Pythagorean triples, prime numbers, divisibility and the
highest common divisor, linear diophantine equations, congruences,
round-robin tournaments and perpetual calendars, multiple functions,
perfect numbers, primitive roots, pseudo-random numbers, decimal
fractions and continued fractions, quadratic reciprocity.
Math
398-399
Seminar in Mathematics (1, 3)
Prerequisites: Math 305, 309, and two additional courses at
the 300-level or above. Under faculty guidance, students will
select a topic in current Mathematical research, write an expository
article on that topic, and give an oral presentation. This seminar is
required of all Mathematics majors who are not doing an Honors Project
within the department. Completion of 398 and 399 fulfills the college
writing requirement.
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| Mathematics
Department Tulane University 6823 St. Charles Ave New Orleans, LA 70118 phone: (504) 865-5727 fax: (504) 865-5063 |
Last Updated:
March 31, 2008
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