Mathematics (MATH) 370

Applied Real Analysis (Revision 1)

MATH 370

Delivery Mode: Individualized Study Online

Credits: 3

Area of Study: Science

Prerequisite: MATH 265, MATH 266, MATH 270, MATH 271 and MATH 365, or equivalent courses from another university.

Faculty: Faculty of Science & Technology

MATH 370 has a Challenge for Credit option.

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Mathematics 370 provides a first course in in Real Analysis. Real Analysis is the branch of mathematics concerned with the analytic properties of the real numbers and real valued functions. Math 370—Applied Real Analysis provides a first course in Real Analysis. This includes units on the real numbers, series, topology, functions, differentiation and integration, and norms and inner products. In addition, Mathematics 370 studies the application of Real Analysis to dynamical systems.

The course content is a carefully arranged series of problems, exercises and theorems that students are expected to work through on their own. Short assignments are assigned at the end of each course unit. A self-directed course project is assigned upon completion of the course units. A midterm and final exam are also used to evaluate students.


This course examines the foundational material of Real Analysis as presented in seven units:

Unit 1 Introduction and Review
Unit 2 The Real Numbers 
Unit 3 Series
Unit 4 Topology of ℝn
Unit 5 Real-Valued Functions 
Unit 6 Differentiation and Integration
Unit 7 Norms and Inner Products
Course Project Dynamical Systems

Learning Outcomes

Upon successful completion of this course, you will be able to

  • demonstrate a foundational understanding of real analysis through the statement, proof and application of key theorems.
  • define the completeness property of the real numbers in terms of limits of sequences, subsequences and the Cauchy sequence.
  • define the concepts of convergence, completeness and compactness in the context of ℝn.
  • differentiate between continuous and discontinuous real-valued functions, as well as between uniform continuity and continuity.
  • distinguish between compactness, the existence of extreme values, and the Intermediate value theorem, and list their implications.
  • demonstrate a foundational understanding of differentiation and integration, culminating with the fundamental theorem of calculus.
  • define and identify normed vector spaces and demonstrate a basic understanding of the topology of normed vector spaces, paying particular attention to inner product spaces.
  • apply the principles of real analysis in the field of dynamical systems.
  • communicate mathematical ideas, and analyses in a clear and organized manner.


The student’s final grade in Mathematics 370 is a composite of the grades achieved on the six assignments, the course project, a midterm examination, and a final examination.

To pass this course, the student must submit all six course assignments. The student must also achieve a grade of at least 60% on each examination, and a course composite grade of at least 60%. The grade weights are summarized below:

Activity Weight
Assignments 1-6 (5% each) 30%
Course Project 25%
Mid-term exam 20%
Final exam 25%
Total 100%
Overall average of 60% (C-) and weighted average of 60% on exams.

Course Materials


Davidson, Kenneth R., & Donsig, Allan P. Real Analysis and Applications: Theory in Practice. New York: Springer, 2010 [print]

Other Materials

Digital course materials include the course orientation, study guide, discussion notes, student manual, and assignments.

Challenge for Credit Overview

The Challenge for Credit process allows you to demonstrate that you have acquired a command of the general subject matter, knowledge, intellectual and/or other skills that would normally be found in a university-level course.

Full information about Challenge for Credit can be found in the Undergraduate Calendar.

Challenge Evaluation

To receive credit for the MATH 370 challenge registration, you must complete the two parts of the challenge exam, written on the same day, or within 2 consecutive days and achieve a grade of at least C- (60%) on both parts.

Activity Weighting
Part 1: Exam 50%
Part 2: Exam 50%
Total 100%

Undergraduate Challenge for Credit Course Registration Form

Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized-study counterparts.

Opened in Revision 1, Jan 28, 2019