根据我院与新加坡南洋理工大学数学系签署的协议, 南洋理工大学数学系每年将从我院本科生中招收若干名直博生。2014年招生考试将于2013年9月18 – 21 日期间在我院进行, 招收对象为我院未报名参加保研的2014本科应届毕业生，具体科目如下:

1)    English Test (EPT，南洋理工大学组织的英语考试，需写一篇英文作文)；

2)    Math Test (TPT syllabus，见下)；

3)    Interview.

有意参加的同学请于9月14日前将报名信息表（见附件）填好发至：

jgqian@xmu.edu.cn

具体时间及地点安排将另行通知。

                                          数学科学学院

                                        2013年8月22日

新加坡南洋理工大学数学系招收直博生报名信息表

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TPT syllabus.

Students can choose either I+II or II+III, that means either

Calculus and Real Analysis + Linear Algebra,

or

Linear Algebra + Algorithms

I.                    Calculus and Real Analysis

I-i)  Limits, continuity and differentiability.

I-ii)  Intermediate Value Theorem,  Rolle’s Theorem, Mean Value Theorem.

I-iii)  Integrability and integrals, substitution rule, integration by parts.

I-iv)  Infinite sequences and series, power series, radius of convergence, absolute  convergence, tests for convergence, Taylor's formula.

I-v)  Elementary differential equations.

II.  Linear Algebra

II-i)  Vector spaces, subspaces, linear independence, basis, dimension, row and column spaces, rank.

II-ii)  Kernels and images. Matrices, inverses, determinants, eigenvectors and eigenvalues, diagonalization.

II-iii)  Systems of linear equations, Gaussian elimination, Gram-Schmidt process.

II-iv)  Quadratic forms, bilinear forms.

III.  Algorithmics

III-i)  Mathematical foundations of algorithm analysis: proofs by mathematical induction,  solving recurrences, analyzing complexity of algorithms.

III-ii)  Algorithm design techniques: divide and conquer, greedy, dynamic programming.

III-iii)  Fundamental graph algorithms: Depth-first search, Bread-first search, spanning trees, shortest paths.

III-iv)  Fundamental data structures: binary search trees, heaps.

III-v)  NP-Completeness and reductions.