Holy Cross Mathematics and Computer Science

MATH 242, section 2 -- Principles of Analysis, Spring 2014

Syllabus and Schedule

Course syllabus
Course schedule

Examples, Solutions, Class Notes, Etc.

Solutions for Problem Set 1.
Solutions for Problem Set 2.
Solutions for Problem Set 3.
Exam 1 solutions.
Solutions for Problem Set 4.
Solutions for Problem Set 5.
Solutions for Problem Set 6.
Exam 2 solutions.
Solutions for Problem Set 7.
Lecture notes on countable and uncountable sets, April 16.
Lecture notes on the Cantor set and function, April 16.
Solutions for Problem Set 8.
Solutions for Problem Set 9.
Exam 3 solutions.
Final Exam solutions

Assignments

Problem set guidelines
Problem Set 1, due: Friday, January 31.
Problem Set 2, due: Friday, February 7.
Problem Set 3, due: Friday, February 14.
Problem Set 4, due: Friday, February 28.
Problem Set 5, due: 5:00pm on Monday, March 17 (Note: change because of missed class).
Problem Set 6, due: Monday, March 24.
Problem Set 7, due: Friday, April 4.
Problem Set 8, due: Friday, April 11.
Problem Set 9, due: Friday, April 25 (Note: this is the Friday of the week after Easter break).

Information and Announcements

Final Exam for this course will be given at 8:00am on Friday, May 9.
Final exam review sheet
Review session for final: Wednesday, May 7 at 7:00pm in Swords 302.
Review sheets from the three midterm exams:
- Exam 1 review sheet
- Exam 2 review sheet
- Exam 3 review sheet
Definitions, etc. you should know for the Final Exam
1. the definitions of set unions, intersections, and complements
2. the definitions of the one-to-one and onto properties of functions
3. the definition of the absolute value of a real number
4. the Well-Ordering Property of the natural numbers
5. the statement of the Principle of Mathematical Induction
6. the definition of a least upper bound for a set of real numbers A (lub(A))
7. the statement of the Least Upper Bound Axiom
8. the ε, n₀ definition of convergence for a sequence
9. the definition of a subsequence of a sequence
10. the ε, δ definition of functional limits (i.e. the precise meaning of lim_x->c f(x) = L)
11. the definition of continuity of f(x) at x = c (be able to state it with limits, or via the ε, δ form)
12. the definition of uniform continuity of f(x) on a subset I of the domain of f (using an ε, δ form)
13. the definition of differentiability of f(x) at x = c and the derivative f '(c)
14. the definition of integrability of f(x) on [a,b] (please refer to the definition given in class on 4/9, not the equivalent version in our text)
15. the definition of a countably infinite set
16. the definition of convergence for an infinite series
17. the definitions of absolute convergence and conditional convergence for an infinite series

Downloading Information

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Last modified: May 9, 2014