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Combinatorics and Optimization


Combinatorics is the study of discrete structures and their properties. It includes coding theory, combinatorial design, enumeration theory, graph theory and polyhedral theory. 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. The functions to be optimized arise in engineering, the physical and management sciences, and in various branches of mathematics. With the emergence of computers, Optimization experienced a dramatic growth as a mathematical theory, enhancing both Combinatorics and classical analysis. In its applications to engineering and management sciences, Optimization forms an important part of the discipline of Operations Research.

Both Combinatorics and Optimization have long been special interests of Canadian mathematicians. Indeed, Waterloo was the first university in the world to have a Department of Combinatorics and Optimization, and it continues to be a leading centre for teaching and research in the theories and applications of these disciplines.

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Honours Combinatorics and Optimization

In conjunction with the common degree requirements in Table I in "Degree Requirements", this program requires at least 26 math half-credits. These overall requirements must include the Faculty core courses outlined in Table II in "Degree Requirements" and the following courses:

All of
C&O 230 Introduction to Combinatorics

One of
C&O 350 Linear Programming
C&O 355 Mathematical Optimization

One of
C&O 330 Combinatorial Enumeration
C&O 342 Introduction to Graph Theory

One of
C&O 351 Network Flow Theory
C&O 367 Nonlinear Optimization
(If C&O 355 is taken, this requirement can be satisfied by taking one of C&O 450-466.)

Three additional half-credits chosen from:
C&O 330 Combinatorial Enumeration
C&O 331 Coding Theory
C&O 342 Introduction to Graph Theory
C&O 351 Network Flow Theory
C&O 367 Nonlinear Optimization
C&O 430 - 466

All of
PMATH 336 Introduction to Group Theory

Two of
AM/PMATH 331 Real Analysis
AM/PMATH 332 Complex Analysis
PMATH 334 Introduction to Rings and Fields
(AM/PMATH 331 may be replaced by one of CS 337, 370)

Two additional 300- or 400-level math half-credits with a course prefix other than C&O

One additional 300- or 400-level math half-credit

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Joint Honours Combinatorics and Optimization

See "Academic Programs" for a complete description of Joint program requirements.

All of
C&O 230 Introduction to Combinatorics

One of
C&O 350 Linear Programming
C&O 355 Mathematical Optimization

Four additional half-credits chosen from:
C&O 330 Combinatorial Enumeration
C&O 331 Coding Theory
C&O 342 Introduction to Graph Theory
C&O 351 Network Flow Theory
C&O 367 Nonlinear Optimization
C&O 430 - 466

All of
PMATH 336 Introduction to Group Theory

Two of
AM/PMATH 331 Real Analysis
AM/PMATH 332 Complex Analysis
PMATH 334 Introduction to Rings and Fields
(AM/PMATH 331 may be replaced by one of CS 337, 370)

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Honours 'X' with Combinatorics and Optimization Minor

See "Academic Programs" for a complete description of Minor program requirements.

All of
C&O 230 Introduction to Combinatorics

One of
C&O 350 Linear Programming
C&O 355 Mathematical Optimization

One of
C&O 330 Combinatorial Enumeration
C&O 342 Introduction to Graph Theory

Two additional half-credits chosen from:
C&O 330 Combinatorial Enumeration
C&O 331 Coding Theory
C&O 342 Introduction to Graph Theory
C&O 351 Network Flow Theory
C&O 367 Nonlinear Optimization
C&O 430 - 466

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Operations Research

Operations Research is the field of mathematics that deals with the problems of management in business and government. It involves constructing mathematical models of complex real world situations and then applying sophisticated techniques to these models in order to make optimal, or near optimal, decisions. The three major components of the discipline of Operations Research are Optimization, Statistics and Computer Science.

The Honours program in Operations Research combines a solid foundation in mathematics with special sequences of courses in economics, business and management science. The mathematics portion of the program includes linear programming, modelling, scheduling, forecasting, decision theory and computer simulation.

In Canada, employers of Operations Research graduates are found in manufacturing, distribution and retail companies, mining, transportation, banking, health services, education, and government agencies. Students proceeding to a Master's of Business Administration degree (MBA) find that a degree in mathematics, emphasizing Operations Research, together with relevant work-term experience, is an excellent preparation for a rewarding career.

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Honours Operations Research

In conjunction with the common degree requirements in Table I in "Degree Requirements", this program requires at least 26 math half-credits, of which at least four must be 400-level math half-credits. These overall requirements must include the Faculty core courses outlined in Table II in "Degree Requirements" and the following courses:

One of
C&O 350 Linear Programming
C&O 355 Mathematical Optimization

All of
C&O 351 Network Flow Theory
C&O 370 Deterministic OR Models
CS 230 Introduction to Computers and Computer Systems
CS 330 Management Information Systems (Alternate: CS 480)
CS 337 Introduction to Numerical Analysis
STAT 331 Applied Linear Models
STAT 333 Applied Probability
STAT 371 Stochastic OR Models
(If C&O 355 is taken, one of C&O 450-466 may be taken instead of C&O 351.)

Five of
C&O 230 Introduction to Combinatorics
C&O 342 Introduction to Graph Theory
C&O 367 Nonlinear Optimization
C&O 437 Cryptography and Communications Security
C&O 450 Combinatorial Optimization
C&O 452 Integer Programming
C&O 453 Network Design
C&O 454 Scheduling
C&O 463 Convex Optimization and Analysis
C&O 466 Continuous Optimization
CS 432 Business Systems Analysis
CS 457 System Performance Evaluation
STAT 332 Sampling
STAT 335 Statistical Process Control
STAT 433 Stochastic Processes
STAT 443 Forecasting

All of
ACC 121 Understanding and Using Financial Accounting Information
ECON 101 Introduction to Microeconomics
M SCI 211 Organizational Behaviour

Two of
ACC 122 Understanding and Using Managerial Accounting Information
ECON 102 Introduction to Macroeconomics
M SCI 311 Organizational Design and Technology
M SCI 432 Introduction to Production Management

Recommended
BUS 352W Marketing I
DRAMA 223 Public Speaking
(BUS 352W is offered by Wilfrid Laurier's School of Business and Economics. See "Business-Related Programs".)

Students enrolled in a Double Honours program in Computer Science and Operations Research must replace the Computer Science courses listed above with the equivalent courses required by Honours Computer Science Major students.

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