美国留学应用数学专业研究报告

　　美国留学应用数学专业研究报告

　　美国留学应用数学专业研究报告一：关于应用数学专业

　　1、应用数学专业介绍：

　　应用数学(Applied Math)：是应用目的明确的数学理论和方法的总称，研究如何应用数学知识到其他范畴(尤其是科学)的数学分枝，可以说是纯数学的相反。包括微分方程、向量分析、矩阵、傅里叶变换、复变分析、数值方法、概率论、数理统计、运筹学、控制理论、组合数学、信息论等许多数学分支，也包括从各种应用领域中提出的数学问题的研究。计算数学有时也可视为应用数学的一部分。

　　2、核心课程：

　　数学分析(analysis)(是数学与应用数学专业的专业基础核心课程，是从初等数学到高等数学过渡的桥梁，是学习其他几乎所有后继专业课程的基础，尤其是复变函数、常微分方程，泛函分析等的学习更要求有良好的数学分析基础。)、几何学、代数学、物理学、概率论与数理统计、微分方程、函数论、离散数学、数学史、数值方法与计算机技术、数学模型、数学实验、教育学与心理学基础、数学教学论、人文社会科学基础。

　　美国本科段核心课程(core courses)：

　　MATH 119 Geometry for Architects

　　MATH 120 Business Mathematics I

　　MATH 121 Business Mathematics II

　　MATH 122 Introduction to Calculus

　　MATH 123 Applied Mathematics

　　MATH 148 Calculus/Precalculus I

　　MATH 149 Calculus/Precalculus II

　　MATH 151 Calculus I

　　MATH 152 Calculus II

　　MATH 230 Introduction to Discrete Mathematics

　　MATH 251 Multivariate and Vector Calculus

　　MATH 252 Introduction to Differential Equations

　　MATH 300 Perspectives in Analysis

　　MATH 332 Matrices

　　MATH 333 Matrix Algebra and Complex Variables

　　MATH 350 Introduction to Computational Mathematics

　　MATH 400 Real Analysis

　　MATH 402 Complex Analysis

　　MATH 405 Introduction to Iteration and Chaos

　　MATH 410 Number Theory

　　MATH 420 Geometry

　　MATH 425 Statistical Methods

　　MATH 426 Statistical Tools for Engineers Descriptive statistics and graphs, probability distributions, random sampling, independence, significance tests, design of experiments, regression, time-series analysis, statistical process control, introduction to multivariate analysis. Same as CHE 426. (3-0-3)

　　Prerequisite： Junior standing.

　　MATH 430 Applied Algebra

　　MATH 431 Applied Algebra II

　　MATH 435 Linear Optimization

　　MATH 453 Combinatorics

　　MATH 454 Graph Theory and Applications

　　MATH 461 Fourier Series and Boundary-Value Problems

　　MATH 474 Probability and Statistics

　　MATH 475 Probability

　　MATH 476 Statistics

　　MATH 477 Numerical Linear Algebra

　　MATH 478 Numerical Methods for Differential Equations

　　MATH 481 Introduction to Stochastic Processes

　　MATH 483 Design and Analysis of Experiments Review of elementary probability and statistics; analysis of variance for design of experiments; estimation parameters; confidence intervals for various linear combinations of the parameters; selection of sample sizes; various plots of residuals; block designs; Latin Squares; one, two and 2k factorial designs; nested and cross factor designs; regression; nonparametric techniques. (3-0-3)

　　Prerequisites： MATH 476 or MATH 474.

　　? Sample Syllabus

　　MATH 485 Introduction to Mathematical Finance This is an introductory course in mathematical finance. Technical difficulty of the subject is kept at a minimum by considering a discrete time framework. Nevertheless, the major ideas and concepts underlying modern mathematical finance and financial engineering will be explained and illustrated. (3-0-3)

　　Credit may not be granted for MATH 485 and MATH 548.

　　Prerequisite： MATH 475 or equivalent.

　　? Sample Syllabus

　　MATH 486 Mathematical Modeling I The primary goal of this course is to provide students the power of using the principles and methods of mathematical modeling for studies of complex systems ain science and engineering. The students will be introduced to the basic notions of the level abstractions, and on how to work on real problems at different levels. The emphasis throughout is on the synergy between the rigorous mathematical approaches, accurate choice of scientific approximation, engineering estimates, and data analysis. A broad range of physical phenomena, engineering applications as well as biological systems will be considered. The use of methods of applied analysis, theoretical physics, probability and statistics will be described. (3-0-3) (C)

　　Credit may not be granted for both MATH 486 and MATH 522.

　　Prerequisites： MATH 461 and MATH 475 (or equivalents).

　　? Sample Syllabus

　　MATH 487 Mathematical Modeling II The formulation of mathematical models, solution of mathematical equations, interpretation of results. Selected topics from queuing theory and financial derivatives. (3-0-3) (C)

　　MATH 488 Ordinary Differential Equations and Dynamical Systems

　　MATH 489 Partial Differential Equations First-order equations, characteristics. Classification of second-order equations. Laplace's equation; potential theory. Green's function, maximum principles. The wave equation： characteristics, general solution. The heat equation： use of integral transforms. (3-0-3)

　　Prerequisite： MATH 461.

　　? Sample Syllabus

　　MATH 491 Reading and Research

　　(Credit： Variable) (C)

　　美国硕士段核心课程(core courses)

　　MATH 500 Applied Analysis I

　　MATH 501 Applied Analysis II

　　MATH 512 Partial Differential Equations

　　MATH 515 Ordinary Differential Equations and Dynamical Systems

　　MATH 519 Complex Analysis

　　MATH 522 Mathematical Modeling

　　MATH 525 Statistical Models and Methods

　　MATH 530 Algebra

　　MATH 532 Linear Algebra

　　MATH 535 Optimization I

　　MATH 540 Probability

　　MATH 542 Stochastic Processes

　　MATH 543 Stochastic Analysis

　　MATH 544 Stochastic Dynamics

　　MATH 545 Stochastic Partial Differential Equations

　　MATH 546 Introduction to Time Series

　　MATH 548 Mathematical Finance I： Discrete Time

　　MATH 550 Topology

　　MATH 553 Discrete Applied Mathematics I

　　MATH 554 Discrete Applied Mathematics II

　　MATH 555 Tensor Analysis

　　MATH 556 Metric Spaces

　　MATH 557 Probabilistic Methods in Combinatorics

　　MATH 563 Statistics

　　MATH 564 Applied Statistics

　　MATH 565 Monte Carlo Methods in Finance

　　MATH 566 Multivariate Analysis

　　MATH 567 Advanced Design of Experiments

　　MATH 568 Topics in Statistics

　　MATH 569 Statistical Learning

　　MATH 577 Computational Mathematics I

　　MATH 578 Computational Mathematics II

　　MATH 579 Complexity of Numerical Problems

　　MATH 581 Theory of Finite Elements

　　MATH 582 Mathematical Finance II： Continuous Time

　　MATH 586 Theory and Practice of Fixed Income Modelling

　　MATH 587 Theory and practice of modeling risk and credit derivatives

　　MATH 589 Numerical Methods for Partial Differential Equations

　　MATH 590 Meshfree Methods

　　MATH 591 Research & Thesis M.S. DegreePermission of Instructor

　　MATH 593 Seminar in Applied Mathematics

　　MATH 594 Special Projects (Credit： Variable)

　　MATH 595 Geometry for Teachers 18 semester hours of an undergraduate mathematics major completed, certification as a mathematics teacher or approval of the instructor. The course is focused on fundamental ideas and methods related to Euclidean and Non-Eu