Course information for Math 215
Introduction to Higher Mathematics

InstructorJennifer Johnson-Leung
 303 Brink Hall

Class Times
MWF 11:30-12:20, JEB 21
Office Hours
Wednesday 1-3pm or By Appointment

Text Krantz The Elements of Advanced Mathematics, Second Edition

Course Description
Mathematics is primarily concerned with two things: numbers and shapes. These are ideas that we investigate even before we learn to read, yet they are the main objects of inquiry for professional mathematicians as well.

This course is in many ways a course of rediscovery. We will examine closely ideas that are often taken for granted. For example, what does it mean for the real numbers to form a line? How do you know that √2 is irrational or that π is transcendental? Most importantly, we will establish a mathematically rigorous notion of proof, and you will learn how to prove mathematical facts.

It is truly the proof that distinguished mathematics from the other sciences. Mathematicians seek not only to understand the objects of their study, but also to prove that their understanding is correct. A proof must be irrefutable. Copious and compelling evidence does not constitute a mathematical proof. A correct proof is truly an achievement for all time. For example, Euclid’s proof of the infinitude of the prime numbers is still taught in mathematics courses around the world, but the science of the ancient Greeks is a curiosity studied only by historians.

Attendance and participation are particularly important in this course. You must keep up with the exercises in order to develop the skills. The analogy with a language course is apt in this regard. You must practice your new “ grammar and vocabulary” in order to develop proficiency with the language of mathematics.

Grading Policies:
Homework: Homework exercises will be assigned in most classes, and you should complete the assignment before the next class period. Collaboration on homework is allowed and encouraged. A subset of the homework exercises will be handed in for grading at the end of each week For the ungraded exercises, there are some solutions in the back of the textbook which can be used to check your work, and we will also go over some of the exercises in class. Students will have the opportunity to explain their solutions to the class.

Quizzes: A quiz will be given approximately every other week as new topics and definitions are introduced. EO students are encouraged to take the quizzes to assess their grasp of new definitions, but EO quizzes will not be graded. Rather 2 extra homework problems will substitute for the quiz grade.
Exams: There will be two midterm exams and a final exam. I usually schedule midterm exams in the evening so that students have plenty of time to write proofs. The first midterm is tentatively scheduled for Tuesday, March 10, and the second for Tuesday, April 28. Our final exam is scheduled for Monday, May 11 at 10am. We will finalize the midterm examination dates within the first two weeks of class. If you have a conflict with the scheduled examination, you must inform me at least two weeks prior to the exam. Exception will be made for illness if a note from the health center (or attending physician) is provided.

Collaboration: You are encouraged to collaborate on solving the problems given as homework. However, the solutions should be written on your own and in your own words. This will aid you in developing the proof-writing skills necessary to be successful on quizzes and exams. There is no collaboration on quizzes or exams.
Blackboard and Electronic Submission of Assignments: Our course webpage will be on Blackboard Enrolled students should have access to the Math 215 page. Students may collaborate on homework in the discussion section, download assignments, find solutions to selected quizzes and exercises, and check grades. A detailed (session by session) syllabus will also be available on Blackboard. If you have trouble logging in to Blackboard, let me know.

If you are an EO student, you are encouraged to submit your work electronically to allow for faster response times. LaTeX is the standard for typesetting mathematics. A great tutorial on LaTeX with instructions to download the free software required can be found at (use the LaTeX link on the left side). I am happy to help you get started with using LaTeX.

If you have a documented need for accommodations such as extra time on exams, you should discuss this with me as soon as possible so that we can make the necessary arrangements.
Point Distribution:

Outline of Topics

We will discuss the ideas below, and others depending on the interest of students. The topics marked with a * will be covered as time allows.

  1. Logic and the Language of Mathematics
  2. Methods of Proof
  3. Sets
  4. Relations
  5. Functions
  6. Infinite Sets, Big and Small
  7. Axiomatic Number Systems
  8. Complex Numbers
  9. * Topology of the real line

This document was translated from LATEX by HEVEA.