General Information:
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- Lectures: MWF 9:30 am – 10:20 am in Classroom Building 313
- Instructor: Paul Arnaud Songhafouo Tsopmene, Office: CW 307.28, Phone: 306-585-4424, Email: pso748@uregina.ca
- Office Hours: MWRF 10:30-11:30 am and T 11:30-12:30 am, or by appointment.
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Textbook: Analysis with an introduction to proof, by Steven Lay, Pearson, 5th edition.
Course Description: You will begin by reviewing the topics contained in Chapters 1 & 2. It is essential that you re-familiarize yourself with all of the topics in these two chapters (I will come back to Section 2.4 as needed). The course will begin in Chapter 3. In this chapter, we survey and study various properties associated with real numbers. From there, we move to Chapter 4, where we consider real sequences and their convergence. This material moves nicely to Chapter 5, in which we return to the theory of functions and consider limits and continuity. Finally, in Chapter 6, we study differentiation from a rigorous point of view.
Content: Topics include
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- The Real Numbers (3.1 through 3.5): Natural Numbers and Induction, Ordered Fields, The Completeness Axiom, Topology of the Real Numbers, Compact Sets.
- Sequences (4.1 through 4.4): Convergence, Limit Theorems, Monotone Sequences and Cauchy Sequences, Subsequences.
- Limits and Continuity (5.1 through 5.4): Limits of Functions, Continuous Functions, Properties of Continuous Functions, Uniform Continuity.
- Differentiation (6.1 through 6.4): The Derivative, The Mean Value Theorem, L’Hospital’s Rule, Taylor’s Theorem.
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Prerequisite: The essential prerequisite for this course is Math 221, but Math 111 is also required to take this course.
Course Outline/Syllabus: More information about this course can be found in the course outline.