Curriculum

本课程涵盖了使用c#编程语言进行计算机编程和算法设计的基本原理. 该类处理基本语言语法, branching, looping, exceptions, I/O, string processing, best practices, 以及编写高质量计算机程序的工具. 它还介绍了将用高级语言编写的程序转换为中间语言的过程，以及操作系统如何加载和执行它. 本课程的学生将能够编写在微软操作系统上运行的基本程序 .. NET框架和开源的Mono.

本课程将透过图解的方法，学习单变量的微分与积分, numerical and symbolic methods. Limits, continuity, derivatives, 我们会用代数方法来研究积分, trigonometric, exponential and logarithmic functions, 包括应用微积分来解决问题. 先决条件:通过分数在微积分安置考试，或系主任的同意.

A continuation of MTH 271, 本课程将包括对积分方法的研究, 应用于代数和超越函数. Solids of revolution, definite and indefinite integrals, Taylor polynomials, sequences and series, 将学习包括应用微积分来解决问题. Prerequisite: C- or better in MTH 271 or acceptable AP examination credit.

本课程将介绍标准数学符号, methods, truth tables, 以及用于确定论证有效性的符号逻辑原理, 处理数学证明的正确符号和结构，包括直接证明和间接证明, mathematical induction, and construction of counter-examples. 将应用于数学领域，如集合论、代数或几何. Prerequisite: C- or better in MTH 272.

本课程将学习矩阵算术的性质, systems of linear equations, determinants, vector spaces, linear transformations, diagonalization, inner products, and applications of these topics. Prerequisite: C- or better in MTH 272.

As a continuation of MTH 272, 本课程将包括向量微积分的学习, three-dimensional calculus, partial derivatives, multiple integrals, differential calculus, 以及向量微积分中其他选定的主题. Prerequisite: C- or better in MTH 272.

本课程将涵盖微分方程与一阶方程的分类, exact differentials, integrating factors, higher order differential equations, method of undetermined coefficients, variation of parameters, operator methods, solution by infinite series, and Laplace transformations. Prerequisite: C- or better in MTH 272. Offered alternate years.

This course will look at the probability and combinatorics; discrete and continuous random variables; the normal, gamma, Chi-square, Poisson, 二项分布的应用. Prerequisite: C- or better in MTH 373 (concurrent enrollment allowed). Offered alternate years.

本课程将学习群体的性质和运作, rings, integral domains, fields, normal subgroups, quotient groups, homomorphisms, and isomorphisms. Prerequisite: C- or better in MTH 313. Offered alternate years.

本课程将介绍实数系统的高级研究, 以及数学分析的思想和证明技巧. 主题包括实数的性质, sequences, series, limits, continuity, and differentiation. Prerequisite: C- or better in MTH 313 and MTH 373. Offered alternate years.

作为所有数学专业两(2)门顶点课程中的第一门, 学生将以小组形式每周会面一次，以回顾本专业的能力, take group-wide assessments, 在他们与教师导师一起工作时，就他们选择的主题完成一份初步研究摘要，然后向他们的同事和教师简要介绍他们的初步发现，以获得反应和反馈. Prerequisite: Senior standing.

作为所有数学专业的两门(2)顶点课程中的第二门, students, working with a faculty mentor, will complete their research from MTH 495 完成一个书面项目，并将他们的发现提交给一个由同行和教师组成的委员会. 鼓励将研究项目纳入总统的本科研究学术展示. Prerequisite: Senior standing.

本课程介绍数值分析的基本算法. 主题可能包括代数方程的数值解, 插值和近似方法, 线性和非线性方程组的近似数值解, 以及数值微分和积分. Prerequisite: C- or better in CSC 104 and MTH 272. Offered alternate years.

本课程将提供包括欧几里得在内的几何演绎系统的一般研究, projective, finite, and other non-Euclidean geometries. Offered alternate years. Prerequisite: C- or better in AMTH 101 or CMTH 101 or MTH 201 or MTH 252 or MTH 271 or equivalent.

A continuation of MTH 387, 本课程将涵盖各种多元概率分布, bias and unbiased estimators, Least Square estimation, ANOVA , Block Designs, 重新审视假设检验和非参数统计的研究. Prerequisite: C- or better in MTH 387. Offered alternate years.

本课程是环内性质和运算的延续, integral domains, fields, quotient rings, groups, subgroups, homomorphisms and isomorphisms. Prerequisite: C- or better in MTH 473 or consent of instructor. Offered alternate years.