MATH 692 Reading, Writing and Discovering Proofs (0.25) LEC 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.

Department Consent Required

MATH 600 Introduction to Mathematical Software for Teachers (0.25) LEC 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. Department Consent Required

MATH 630 Foundations of Probability (0.50) LEC 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. Department Consent Required

MATH 640 Number Theory for Teachers (0.50) LEC 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. Department Consent Required

MATH 647 Foundations of Calculus I (0.50) LEC 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. Department Consent Required

MATH 648 Foundations of Calculus II (0.50) LEC 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. Department Consent Required

MATH 650 Mathematical Modeling with Differential and Difference Equations (0.50) LEC 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. Department Consent Required

MATH 660 Explorations in Geometry (0.50) LEC 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. Department Consent Required

MATH 670 Mathematical Connections: Real World Problems in Mathematics I (0.25) LEC Course ID: 013839

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. Topics: The course is one of four similar courses that will consist of either 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. Department Consent Required

MATH 671 Mathematical Connections: Real World Problems in Mathematics II (0.25) LEC Course ID: 013838

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. Topics: The course is one of four similar courses that will consist of either 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. Department Consent Required

MATH 672 Mathematical Connections: Real World Problems in Mathematics III (0.25) LEC Course ID: 013837

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. Topics: The course is one of four similar courses that will consist of either 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. Department Consent Required

MATH 673 Mathematical Connections: Real World Problems in Mathematics IV (0.25) LEC Course ID: 013836

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. Topics: The course is one of four similar courses that will consist of either 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. Department Consent Required

MATH 674 Special Topics in Mathematical Connections (0.50) LEC 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.

Department Consent Required.

1 Mathematical Finance I

2 Mathematical Finance II

MATH 680 History of Mathematics (0.50) LEC 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. Department Consent Required

MATH 681 Problem Solving and Mathematical Discovery (0.50) LEC 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. Department Consent Required

MATH 690 Summer Conference for Teachers of Mathematics (0.25) SEM 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. Department Consent Required

MATH 698 Reading Course in Mathematics for Teachers (0.50) RDG Course ID: 014236

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

MATH 699 Master of Mathematics for Teachers Capstone (0.50) RDG 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.

Department Consent Required.

Source: http://www.cemc.uwaterloo.ca/mmt.html

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