### Graduate Studies and Postdoctoral Affairs (GSPA)

Needles Hall, second floor, room 2201

Telephone 519 888-4567 ext. 35209

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For more detailed course information, click on a course title below.

Course ID: 013923

This course exposes students to the technical tools that professional mathematicians use. The software presented in the course will enhance each student's communication, presentation, visualization, and problem-solving skills. The course will also take a brief look at the history of mathematical communication and its impact on the development of the subject.

Course ID: 013831

This course will explore the basic properties of probability focusing on both discrete and continuous random variables. Topics include: Laws of probability, discrete and continuous random variables, probability distributions, mean, variance, generating functions, Markov chains, problem solving, history of probability.

Course ID: 014701

This course discusses some of the mathematical and scientific aspects of empirical, or data-based, problem solving. Topics will include methods for the design of experiments and surveys, and the analysis of data using statistical models. Examples will illustrate the application of these methods to data-based problems in science, health, business and industry.

Course ID: 014804

This course explores the foundations of linear algebra and some of its applications. An emphasis will be placed on the development of mathematical thinking and the importance of proof in mathematical teaching. Topics include: matrices, linear mappings, vector spaces, determinants, diagonalization, inner products, the Fundamental Theorem of Linear Algebra, and the method of least squares.

Course ID: 014212

This course explores the many fascinating properties of the natural numbers. Topics include: the Euclidean algorithm, congruences and modular arithmetic, primitive roots and quadratic residues, sums of squares, multiplicative functions, continued fractions and Diophantine equations, and rational approximations to real numbers.

Course ID: 014340

This course explores the intersection between mathematics and computer science by examining general methods for solving problems efficiently. We will study a variety of algorithm design techniques for problems in diverse application areas and use mathematical models to compare algorithms. Students will be introduced to "big ideas" from computer science, such as the generalization and reuse of previous solutions, and the notion of limits to the power of computation.

Course ID: 014805

The connections between mathematics and computer science are varied and deep. This course will introduce students to foundational ideas in computer science and their relationship to foundational ideas in mathematics through the use of a functional programming language designed for education. No prior experience with programming is required, though students with exposure to popular programming languages will also benefit from this alternate approach.

Course ID: 014806

This course will use mathematics to study the foundations of problem solving and computation. A decision problem (answering "yes" or "no") can be characterized as a set of strings of characters encoding inputs that yield "yes" answers, and a computer can be characterized as a simple mathematical machine model that processes strings of characters. By studying properties of classes of problems of increasing complexity, we will be able to establish relationships among classes, membership in classes, and hard problems for classes. The course will culminate in the examination of classes and models that correspond to the power of computers, and the demonstration that there exist problems that cannot be solved.

Course ID: 013841

This course will explore the foundations of differential calculus, the role of rigor in mathematics, and the use of sophisticated mathematical software. Topics include: A brief primer on logic and proof, axiom of choice and other ideas from set theory, convergence of sequences and the various forms of the completeness axiom for R, detailed study of limits, continuity and the Intermediate Value Theorem, fundamentals of differentiation and the importance of linear approximation, role of the Mean Value Theorem, the nature and existence of extrema, Taylor's Theorem and polynomial approximation, MAPLE as a tool for discovery.

Course ID: 013840

This course explores the foundations of integral calculus and the use of series in approximating the basic functions of mathematics. Topics include: Understanding the Riemann Integral and its flaws, the idea of Lebesque, the geometric meaning of the Riemann-Stieltjes integral, the Fundamental Theorem of Calculus, numerical integration, numerical series, uniform convergence of functions and the extraordinary nature of power series, Fourier Series.

Course ID: 014058

Solving and interpreting differential and difference equations motivated by a variety of systems from the physical and social sciences. Analytical solutions of standard linear and non-linear equations of first and second order; phase portrait analysis; linearization of non-linear systems in the plane. Numerical and graphical solutions using mathematical software.

Course ID: 013833

This course is designed to allow the student to discover fundamental facts about geometry through the interactive use of mathematical software. Possible topics include: An introduction to affine, projective and non-Euclidean geometry, conic sections in projective geometry, inversion in circles, the Theorems of Desargues, Pappas and Pascal.

Course ID: 015053

This course explores the Euclidean geometry of triangles and circles from elementary to advanced settings. The course also briefly discusses three-dimensional geometry. An emphasis is placed on proof, on problem solving, on problem creation in a geometric context, and on aspects of teaching geometry. Where possible, problems that combine multiple areas of mathematics are used.

Course ID: 014213

This course is intended to give the student insight to an important area of mathematics and how it connects with problems in the real world. The course will consist of either a one six week module, or two three week modules each introducing a separate though possibly related area of mathematics. The emphasis will be on how the mathematics is used in a real world context.

Course ID: 013842

We explore the who, where, when and why of some of the most important ideas in mathematics. Topics include: William T. Tutte and Decryption, Euclid and the Delian Problem, Archimedes and his estimate of Pi, Al Khwarizmi and Islamic mathematics, Durer and the Renaissance, Descartes and Analytic Geometry, and Kepler and Planetary Motion.

Course ID: 013835

This course aims to develop the student's mathematical problem solving ability. Common heuristics such as problem modification, patterning, contradiction arguments and exploiting symmetry will be examined. A wide range of challenging problems from various branches of mathematics will provide the medium through which these important principles and broad strategies are experienced.

Course ID: 013834

This intense 3-day workshop focuses on the integration of problem solving technology into the curriculum and enrichment activities. The Workshop is suitable for teachers from all over the world.

Course ID: 009357

Objectives: To develop the vocabulary, techniques and analytical skills associated with reading and writing proofs, and to gain practice in formulating conjectures and discovering proofs. Emphasis will be placed on understanding logical structures, recognition and command over common proof techniques, and precision in language.
Topics Include: rules of formal logic, truth tables, role of definitions, implications, sets, existential and universal quantifiers, negation and counter-example, proofs by contradiction, proofs using the contrapositive, proofs of uniqueness and induction.

Course ID: 014236

Students will undertake a reading, research and writing project on a mathematical topic of interest to teachers.

Course ID: 013832

The capstone course is designed to give students an opportunity to showcase the knowledge they have gained and to provide a forum for bringing that knowledge into their own classroom. As part of this course students will design a mini-course on an approved subject in mathematics.

Needles Hall, second floor, room 2201

Telephone 519 888-4567 ext. 35209

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1