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组合与优化哲学博士-代数组合

Doctor of Philosophy in Combinatorics and Optimization - Algebraic Combinatorics

滑铁卢大学

University of Waterloo

CA加拿大

  • 学历文凭

    学历文凭

    Ph.D.

  • 专业院系

    专业院系

    Department of Combinatorics and Optimization

  • 开学时间

    开学时间

  • 课程时长

    课程时长

  • 课程学费

    课程学费

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国际学生入学条件

A Master's degree in combinatorics and optimization, or in a closely related field, with a minimum 89% average in Master's level coursework.
Completion of a master's thesis.
It is essential that the application for admission into the PhD program contains evidence of research ability or potential.
Three references, normally from academic sources
Proof of English language proficiency, if applicable. TOEFL 90 (writing 25, speaking 25), IELTS 7.0 (writing 6.5, speaking 6.5)
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  • 雅思总分:7
  • 托福网考总分:90
  • 托福笔试总分:160
  • 其他语言考试:PTE (Academic) - 63 (writing 65, speaking 65)

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课程简介

在代数组合中,我们可以使用代数方法来解决组合问题
Combinatorics is the study of discrete structures and their properties. Many modern scientific advances have employed combinatorial structures to model the physical world, and recent advances in computational technology have made such investigations feasible. In particular, since computers process discrete data, combinatorics has become indispensable to computer science. Optimization, or mathematical programming, is the study of maximizing and minimizing functions subject to specified boundary conditions or constraints. With the emergence of computers, optimization experienced a dramatic growth as a mathematical theory, enhancing both combinatorics and classical analysis. The functions to be optimized arise in engineering, the physical and management sciences, and in various branches of mathematics. The PhD involves about two years of grad courses followed by research and a dissertation, and typically lasts four years.<br><br>In algebraic combinatorics we might use algebraic methods to solve combinatorial problems, or use combinatorial methods and ideas to study algebraic objects. The unifying feature of the subject is any significant interaction between algebraic and combinatorial ideas. As a simple example, to solve an enumeration problem one often encodes combinatorial data into an algebra of formal power series by means of a generating function. Algebraic manipulations with these power series then provide a systematic way to solve the original counting problem. Methods from complex analysis can be used to obtain asymptotic solutions even when exact answers are intractable. As another example, group theory and linear algebra are used to understand the structure of graphs. Most graphs have no nontrivial symmetries (automorphisms) -- graphs with many symmetries are highly structured and have applications in design theory, coding theory, and geometry. For any graph, the eigenvalues of its adjacency matrix encode a great deal of structural and enumerative information about it.
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学校排名

  • 排名

    世界排名201

    数据源:泰晤士高等教育世界大学排名

关于滑铁卢大学

滑铁卢大学是加拿大滑铁卢市的一家著名大学,是一所以研究为主的中等大小的公立大学,创建于1957年。以数学、计算机科学、工程学而闻名。该校位于安大略省的西南面的滑铁卢市,占地面积约为1000英亩。滑铁卢大学成立至今,仅数十年便跻身加拿大名校之列,是加拿大发展最快的学校。2011年到2013年,该校一直稳居麦克林杂志评选的加拿大综合性大学排名的第三位,是北美地区最优大学之一,其数学,计算机科学和工程学科教学水平居世界前列。特别是做为北美地区第一个经认可建立数学系的大学,拥有世界上最大的数学系以及世界上最大的合作办学项目。学校共授予100多个本科学位专业,28种硕士及博士学位专业,学校的代表队曾多次获得ACM 国际大学生程序设计竞赛的冠军。

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