Holy Cross Mathematics and Computer Science
MATH 242, Principles of Analysis, Fall 2004
Syllabus and Schedule
Examples, Class Notes, Etc.
Assignments
- Problem Set 1 -- From Lay, Section 1/4cef,6ad,7,9fgh,11;
Section 2/3,5,6,7,8,9; Section 3/4,5,6abc,8,9; Section 4/7, 12
-- Due: Friday, September 10.
- Discussion 1 --
Due: Monday, September 13
- Problem Set 2 -- From Lay, Section 5/3,4,9,11,12,14,16;
Section 6/3,5abcd,7,8; Section 7/3,4,8,9,10,12,13,20 --
Due: Friday, September 17.
- Problem Set 3 -- From Lay, Section 8/3abe,4,11; Section 10/3,6,7,11,14,15,
16,17,18 -- Due: Friday, September 24.
- Discussion 2 --
Due: Wednesday, October 6
- Problem Set 4 -- From Lay, Section 11/8,9; Section 12/3efgh,4efgh,7,8;
Section 16/4abd,5c,6c,7,8,12. Due: Friday, October 15
- Problem Set 5 -- From Lay, Section 17/4, 5bdfhjl, 6, 13, 18;
Section 18/3abd, 6, 10; Section 19/4, 5. Due: Monday, October 25
by 5:00pm.
- Problem Set 6 -- From Lay, Section 20/3aceg,4ac,6,7,8,9,11,14
Due: Friday, November 5
- Problem Set 7 -- From Lay, Section 21/3,4,8,9,11,13;
Section 22/4,5,6,7,8,9. Due: Friday, November 12
- Discussion 3 --
Due: Monday, November 15
- Problem Set 8 -- From Lay, Section 25/3ae,5,7,13,16;
Section 26/3,4,6,7,8. Due: Friday, November 19
- Problem Set 9 -- From Lay, Section 27/3bdfh,5,6,12,13; Section
29/4,5,7,8,9,10. Due: Monday, November 29, no later than
5:00pm
Information and Announcements
- Final Exam for this course: 8:30 to 11:30 am on Wednesday, December 15.
- Review session: Monday, December 13, 7:00pm - ?, in SW 328.
- To help you prepare:
- Definitions you should know:
- The definitions of the
truth tables for the logical connectives: negation (``not''),
conjunction (``and''), disjunction (``or''), implication
(``if, then''),
and equivalence (``if and only if'') and be able
to work out a truth table for a compound statement like
the ones in Example 3.12 in the book.
- The definitions of reflexivity, symmetry, and
transitivity for a relation, and what an equivalence relation is
- The definitions of what it means for a function to be
injective or surjective.
- The definition of what it means for sets S,T
to be equinumerous
- The definitions of what it means for a set S
to be countable or denumerable.
- The definition of an upper bound for a set S in
R.
- The definition of the least upper bound (supremum)
for a set S in R.
- The definition of the statement ``the sequence
xn converges to L in
R.''
- The precise definition of the statement ``limx->c f(x) = L''
- The precise definition of the statement ``f(x) is continuous at c''
- The precise definition of the what it means for a function
to be differentiable at x = c and the derivative
f'(c).
- The precise definition of the upper and lower integrals
U(f) and L(f)
of a function on [a,b], and what it means for a function
to be integrable on [a,b]
- The precise definition of the statements ``the infinite series
with terms an converges'', or ``converges absolutely''.
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 most 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: December 16, 2004