MAT 266 - Introduction to Real Analysis
This course provides a rigorous introduction to the concepts of axiomatics, sets, measures, functions, sequences, series, integration/differentiation and metric spaces. Emphasis will be placed on writing mathematics clearly, especially regarding proofs. Recommended for Mathematics majors or Computer Science and Engineering Science students as advised.
Prerequisite: MAT 281 Calculus III or permission of the instructor
3 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Prove one set is a subset of another.
2. Prove two sets are equal.
3. Verify that a function is one-to-one and/or onto.
4. Prove theorems about the functions and inverse functions.
5. Use the principle of mathematical induction.
6. Define continuity of a function at a point.
7. Define a bound on a set.
8. Find infima and suprema of a set.
9. Identify sets as countable or uncountable.
10. Calculate the measure of a set.
11. Define the Cantor Set.
12. Define a sequence and be able to identify the following:
c. isolated points
d. accumulation points
f. the Cauchy property
13. Define pointwise and uniform convergence for sequences of functions.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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