Douglas College wordmark
Facebook logo Twitter logo Instagram logo Snapchat logo YouTube logo Wordpress logo

Registration for the Fall 2019 semester begins June 25.  Watch your email for more details.

back to search

Introduction to Mathematical Analysis

Course Code: MATH 2245
Faculty: Science & Technology
Department: Mathematics
Credits: 3.0
Semester: 15 weeks
Learning Format: Lecture, Tutorial
Typically Offered: Summer
course overview

A one-semester introduction to analysis for students who have successfully completed the first year of calculus (six credits). This course presents foundation concepts in analysis which lay the groundwork for further study in pure and applied mathematics, in particular real analysis courses. It is normally required material for mathematics majors. Topics studied include the nature of proof, set theory and cardinality, the real numbers, limits of sequences and functions, continuity, formal coverage of the derivative and the mean value theorem, Taylor’s theorem, the Riemann integral, the fundamental theorem of calculus, and topics in infinite series.

Course Content

1. Logic and Proof:

  • elements of logic
  • various proof techniques

2. Sets and Functions:

  • set algebra
  • relations and functions
  • introduction to cardinality

3. The Real Numbers: 

  • natural numbers
  • induction
  • definition of field
  • notion of completeness

4. Sequences: 

  • subsequences
  • convergence
  • monotonicity
  • Cauchy sequences

5. Limits and Continuity:

  • function limits
  • continuity and its properties
  • uniform continuity

6. Differentiation: 

  • definition and properties of derivative
  • mean value theorem
  • Taylor's theorem

7. Integration: 

  • Riemann integral and its properties
  • the fundamental theorem of calculus

8. Infinite series:

  • definition of convergence
  • convergence testing
  • introduction to power series

Methods of Instruction

Lectures, Tutorials

Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy.  The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester.  Evaluation will be based on the following criteria:

Problem sets, quizzes, assignments: 0-40%
Tutorials: 0-10%
Term tests: 20-60%
Final exam: 30-40%

Learning Outcomes

The student who successfully completes this course will:

  • use the rules of logic to study the way in which mathematical arguments are constructed
  • analyze the structure of mathematical proofs and illustrate proof techniques by means of examples
  • use set theory to construct mathematical proofs
  • examine the structure and properties of the real number system
  • use the definition of convergence of a sequence to determine the limit of a sequence
  • prove and work with theorems relating to properties of convergent sequences
  • define the limit of a function and continuity of a function 
  • prove and work with theorems relating to continuous functions beyond those found in elementary calculus
  • define the derivative of a function and establish properties of differentiable functions
  • define the Riemann integral and establish properties of integrable functions
  • define infinite series and develop tests to determine whether an infinite series is convergent or divergent
  • define a power series and establish basic convergence properties of power series

course prerequisites

MATH 1220  (with a grade of C+ or better)

curriculum guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester/year of the course, consider the previous version as the applicable version.

course schedule and availability
course transferability

Below shows how this course and its credits transfer within the BC transfer system. 

A course is considered university-transferable (UT) if it transfers to at least one of the five research universities in British Columbia: University of British Columbia; University of British Columbia-Okanagan; Simon Fraser University; University of Victoria; and the University of Northern British Columbia.

For more information on transfer visit the BC Transfer Guide and BCCAT websites.

assessments

If your course prerequisites indicate that you need an assessment, please see our Assessment page for more information.