Simon Fraser University
Engaging the World

Course Outlines

Fall 2019 - MATH 603 G001

Foundations of Mathematics (4)

Class Number: 4131

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 3 – Dec 2, 2019: Tue, 4:30–8:20 p.m.
    Burnaby

  • Prerequisites:

    Acceptance into the MSc program in mathematics education or permission of the department. Graduate students in the Department of Mathematics cannot take this course to satisfy their degree requirements.

Description

CALENDAR DESCRIPTION:

Crises in mathematics, their historical and philosophical background and their resolution.

COURSE DETAILS:

The course will focus on "great theorems" and "big ideas" of mathematics. The "great theorems" to be "covered" will be chosen from the following list:

  • The Fundamental Theorem of Arithmetic
  • The Fundamental Theorem of Algebra
  • The Fundamental Theorem of Calculus
  • Pythagoras and friends
  • The three Greek construction problems
  • The Four Color Theorem  
The "big ideas" include, but not limited to
  • Numbers (journey from Whole to Transfinite);
  • Logarithms: Sets; Induction and Recursion; Zero and Infinity;
  • Functions and Variables;
  • Symmetry  
We will engage in exploring underlying mathematical concepts and engage in discussion on what makes ideas or theorems "big", "great" or "fundamental". We will explore historical and philosophical background that led to the development of several "new" mathematical concepts and ideas. Moreover, we will engage in mathematical problem solving to experience mathematics in the making, rather than as a finished product.

COURSE-LEVEL EDUCATIONAL GOALS:

Students explore foundational ideas in mathematics and great theorems
Students enhance personal problem solving skills
Students get initial introduction to mathematics education research

Grading

  • Homework Assignments 60%
  • Project (the topic will be chosen in consultation with instructor) focused on either a detailed exploration of a mathematical idea through history or of a mathematician's work and life, together with an in-class presentation. 40%

Materials

REQUIRED READING:

Readings will be provided by the instructor

RECOMMENDED READING:

Imre Lakatos (1976) Proofs and Refutations: the Logic of Mathematical Discovery, Cambridge: Cambridge University Press.
ISBN: 978-0521290388

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS