Spring 2018

Math 1250 Math Thinking in the Real World

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General Information, Syllabus, Assessment and Test Dates

What is this course?

This is a course about discovering the true nature of mathematics and how some of the greatest ideas in mathematics are used in our modern-day world. The course emphasizes strategies of thought and analysis in examining topics ranging from prime numbers to infinity, the fourth dimension, chaos and fractals. The class is in seminar format - most class time will be spent in discussion and group activities. Students are important active participants in the teaching and learning process! An important component of the class is that it should be fun. The ideas discussed in the course are among the most beautiful and elegant of the ideas of humankind. Although Math 1200 College Algebra is a stated prerequisite, the course does not require students to have mastered all the material of College Algebra. What it does require is an ability and commitment to think hard and logically about all kinds of interesting questions.


We study some of the greatest ideas in mathematics that are often hidden from view in lower division courses. We aim to discover the innate beauty and power that mathematical thinking provides for exploring a variety of aspects of the world around us, and to emerge from the course with an understanding of what it is that mathematicians do.

Student Learning Objectives

  1. Students will be able to demonstrate the ability to recall accurately definitions of concepts in the course, e.g., Fibonacci numbers, prime numbers, one-to-one correspondence, golden ratio, platonic solids, topological equivalence, Möbius band, Euler circuit, planar graph, fractal.
  2. Students will be able to demonstrate the ability to prove basic results about fundamental concepts of the course, e.g., the infinity of primes, the irrationality of the square root of a prime, the countability of the rationals, the uncountability of the reals, the Theorem of Pythagoras, the Art Gallery Theorem, an outline of the Brouwer Fixed Point Theorem, the Hot Loop Theorem.
  3. Students will be able to demonstrate the ability to recognize when and how to apply important theorems.
  4. Students will be able to demonstrate the ability to work with and devise examples that illustrate basic concepts of the course.
  5. Students will be able to demonstrate the ability to translate a real life problem into mathematical language and recognize which mathematical tools to apply to solve the problem.
  6. Students will be able to demonstrate an appreciation for the beauty and power of mathematics.


This class addresses the Scholarship and Knowledge, Intellectual Inquiry and Communication, and Community Building aspects of the Five Dimensions of the Saint Louis University Experience.


Chapter 1: Fun and Games: An Introduction to Rigorous Thought
Chapter 2: Number Contemplations (2.1 - 2.6)
Chapter 3: Infinity (3.1 - 3.3)
Chapter 4: Geometric Gems (4.1 - 4.5, 4.7)
Chapter 5: Contortions of Space
Chapter 6: Modeling Our World Through Graphs (6.1 - 6.3)
Chapter 7: Chaos and Fractals


1.Homework and Projects25%
2.Class participation15%
4.Final Examination24%

Test Schedule

Test 1: Friday, February 9
Test 2: Friday, March 9
Test 3: Wednesday, April 18
Final: Wednesday, May 9 at 12 p.m.