Holy Cross Mathematics and Computer Science
MATH 242, section 1 -- Principles of Analysis, Spring 2011
Syllabus and Schedule
Examples, Solutions, Class Notes, Etc.
Assignments
- Problem set guidelines
- Problem Set 1 -- due: Friday, February 4.
- A portion: Section 1.1/5bc, 8abef, 9, 10; Section 1.2/1cdefghi, 8, 9, 10bc. (Give complete
justifications for all answers.)
- B portion: Section 1.1/2abd, 3, 4; Section 1.2/5, 6, 12, 14.
- (See guidelines above for what the two portions mean!)
- Problem Set 2 -- revised as of February 9, due: Friday, February 11.
- A portion: Section 1.3/11, 13ab, 16; Section 1.4/6, 12.
- B portion: Section 1.3/7, 8, 9, 10 (these are related!); Section 1.4/2b, 3, 10.
- Problem Set 3 -- due: Friday, February 18.
- A portion: Section 1.5/1, 2, 3, 23.
- B portion: Section 1.5/4, 7, 8, 9, 13, 22.
- Note: For true/false questions like 1 and 13, if you think the statement
is false, give a counterexample (an explicit set, or function, or ... that
shows the statement is false in general); if you think the statement is
true, give a reason (for instance, cite a theorem from the text
that shows that fact, or give a short proof).
- Problem Set 4 -- due: Friday, March 4.
- A portion: Section 2.1/1, 13, 15; Section 2.2/2, 3, 6ace, 7, 17ac; Section 2.3/2.
- B portion: Section 2.1/2acej, 4, 11; Section 2.2/13, 19; Section 2.3/6,11
- Problem Set 5 -- due: Friday, March 18.
- A portion: Section 2.3/7; Section 2.4/5cde; Section 2.5/2,3,8.
- B portion: Section 2.3/15; Section 2.4/3,6a; Section 2.5/12,13,14; Section 3.1/2aj.
- Problem Set 6 -- due: Friday, March 25.
- A portion: Section 3.1/2lmo,5; Section 3.2/6; Section 3.4/1adgij,4,7,8a.
- B portion: Section 3.1/6,9; Section 3.2/3,7,9; Section 3.4/2,3.
- Problem Set 7 -- due: Friday, April 8.
- A portion: Section 3.5/2,6,7,10; Section 3.6/1ac,2c; Section 4.1/2a,10,12.
- B portion: Section 3.5/3,15,16,22,23; Section 3.6/4; Section 4.1/11,19.
- Problem Set 8 -- due: Friday, April 15. -- Note: two problems from Section 5.1 have been postponed to the next Problem Set
- A portion: Section 4.2/3,6; Section 4.3/2ace,3,9; Section 5.1/1.
- B portion: Section 4.2/8abcef,10; Section 4.3/4,6,10,11,16,26.
- Problem Set 9 -- due: Friday, April 29.
- A portion: Section 5.1/10,11,14; Section 5.2/1, 4 (see directions for questions 1 - 4 on page 180), 5ad; Section 5.3/2; Section 5.4/1ace,2
- B portion: Section 5.1/12,13; Section 5.2/12, 13; Section 5.3/4,5,9,10; Section 5.4/8;
Extra Problem: Show that the Cantor function (see class notes from
Monday, 4/11) is continuous on [0,1] and differentiable at all x in the complement of the Cantor set.
- Optional Problem Set 10 -- due: no later than 5:00pm on Friday, May 13. Section 6.1/1cdf, 4cdeg, 8, 11, 12a; Section 6.2/1acegi, 5ad, 6, 8, 9; 6.3/2ace. Note: This is an optional assignment that will be treated as Extra Credit on the Problem Set average for the semester. Even if you do not have the time or the energy to complete all of these problems, it will be to your advantage to attempt some of them--both for the extra points you may earn and for the practice on examples like this for a probable question on the Final Exam.
Information and Announcements
- Final Exam for this course will be given:
Tuesday, May 17, 2011, 3:00 - 5:30pm, in Swords 359 -- Final exam review sheet
- Review Session -- Sunday, May 15 at 2:00pm in Swords 359.
- Here are the review sheets for the three midterm exams as well
- Definitions you should know for the Final Exam:
- the definitions of set unions, intersections, and complements
- the definitions of the one-to-one and onto properties of functions.
- the definition of the absolute value of a real number.
- the Well-Ordering Property of the natural numbers.
- the definition of a least upper bound for a set A
(sup(A)),
- the statement of the Axiom of Completeness
- the definition of a countably infinite set
- the definition of convergence for a sequence
- the definition of a subsequence of a sequence
- the definition of functional limits (i.e. the precise meaning
of limx->c f(x) = L)
- the definition of continuity of f(x) at x = c.
- the definition of differentiability of f(x) at x = c.
- the definition of integrability of f(x) on [a,b].
- the definition of convergence for an infinite series.
- the definitions of absolute convergence and conditional convergence
for an infinite series
Related Links
- Biographical information on Bernhard
Riemann
- Biographical information on Georg
Cantor
- Biographical information on Karl
Weierstrass
- Biographical information on Bernard
Bolzano
Downloading Information
The links for assignments and other handouts shown above lead in some cases
to documents in .pdf format. To read and print these, you will need to have
Adobe Acrobat Reader installed on your computer. This is available at no
cost from Adobe.
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Last modified: May 18, 2011