Transition to advanced mathematics, Spring 2010

Instructor: Milena Hering
Class time and room: Monday, Wednesday, Friday 12:00 - 12:50 in MSB411
Office: MSB M322
Office hours: Wednesday 11-11:50, Thursday 2:30-3:30, by appointment, or you can just drop by my office.
Phone: 486-3120
E-mail: hering@math.uconn.edu

The Syllabus.

Some general comments about homework:

• Appearance: It should be stapled and neatly written (double spaced). Better start a new page for a new problem, unless you are sure it will fit.
• Rewritten homework: due in the class after the homework was returned. Please make a table with the problems you have rewritten, a column with your old grade, and a column for your extra points.
• Turn in Homework in class. I do not accept homework via e-mail.

Some comments about writing and proving:

• When you explain your solution do not assume that I know what the problem is and how to do it. You should write it up in a way that your math friend can happily follow what you are doing. This starts with writing down what you want to prove. Or what direction you are proving.
• When you use a variable, make sure you introduced it and that you told the reader what sort of object it denotes.
• If you need to prove something for numbers in a certain range (e.g. all reals greater than 2 and less than 4, or for all natural numbers) it is not sufficient to show that the statement holds for one example. This example tells you nothing about whether the statment holds for the other numbers. Of course, often, doing an example will help you find a proof for the general statement you want to prove.
• In a "proof to grade" exercise, you are not supposed to fix the proof, but you should point out what makes the proof not correct (if it is not correct). You need not repeat the claim for these problems.

  Check out this NYT opinionator on numbers.

  Schedule
  
  

  Class Period	Event	To read	Homework	Homework to turn in
  Wednesday, January 20		Syllabus, Preface to the student, 1.1 and 1.2	1.1: 2gl, 3ejk, 4en, 7, 8de, 10bdfi, 12	HW1 1.1: 2g, 10b, 12 1.2: 9de (write essay type proof as on page 15, second paragraph),12 1.3: 4, 6ce 1.4: 7gj, 8 1.5: 10,11,12
  Friday, January 22		1.3	1.2: 1ceh, 4bd, 6e, 9de, 12, 14a
  Monday, January 25		1.4	1.3: 1hkm, 4, 5dhij,6ce,7e
  Wednesday, January 27		1.5	1.4: 5abe, 6a,7adf, 11
  Friday, January 29		1.6	1.5: 3dg, 4a,9
  Monday, February 1	Add/Drop	1.6	1.5: 3c, 6a, 7a	HW2 1.5: 7b 1.6: 3,4,7af, 8abch 1.7: 2c, 3c, 6b
  Wednesday, February 3	HW 1 due	1.7 (especially the first few pages)	1.6: 1di, 2ad, 5bf, 6ac
  Friday, February 5		1.7 (especially the second half)	1.7: 1a, 2b, 3a
  Monday, February 8		2.1	1.3, 5a-k: negate each statement and prove or give counterexample.	HW 3 1.6: 5g (do the problem as in the book, then negate the statement and prove the negated statement or provide a counterexample for it). 1.7: 9b, 12ade
  Wednesday, February 10	class cancelled
  Friday, February 12	HW 2 due	Studyguide	8abc, 9a, 11f
  Monday, February 15	no Midterm
  Wednesday, February 17	Midterm
  Friday, February 19
  Monday, February 22		2.2 and 2.3	2.1: 1ad, 3acegi, 4ackj, 5a, 9ac 2.2: 1acegi, 2acegi, 3abcdefhk, 10a, 11a, 13a, 14a, 16g	HW4 2.1: 6c,11,19abfg 2.2: Prove 2.7 g), 11d, 12d, 17cf 2.3: 14,19, 20cde See Homework 4.
  Wednesday, February 24	HW 3 due	2.4	2.3: 1adg, 2, 6a, 8abc, 13 2.4: 1abc, 2ab, 3a, 4f
  Friday, February 26		2.5	2.4: 8fhi, 9a
  Monday, March 1			2.5: 4,5	HW5 2.4: 8s, 15acd 2.5: 15a Homework 5.
  Wednesday, March 3	HW 4 due		2.4: 8clm
  Friday, March 5	HW 3 rewrites due	3.1
  Monday, March 8	Spring break
  Wednesday, March 10	Spring break
  Friday, March 12	Spring break
  Monday, March 15		3.2	3.1: 1d, 5, 6b, 8b, 9a, 12, 13, 20fg	HW 6 carefully read the notes about Homework on the top of this page Homework 6.
  Wednesday, March 17	HW 5 due	3.3	3.2: 1bc, 2bf, 4a, 8, 12ac, 16cde
  Friday, March 19		4.1	3.3: 1abc, 3b, 6a, 8a, 3c,8b,15a
  Monday, March 22		4.2	4.1: 3bi, 4ab, 6a, 7b, 9ab	HW 7 Homework 7.
  Wednesday, March 24		4.3	4.2: 1bf, 2bdf, 14bh, 15a, 4.3: 1bd, 8b
  Friday, March 26		4.3	Start working on HW 7.
  Monday, March 29	HW 4 rewrite due, HW 6 due		4.3:3bcd, 10abcd, 14ab	Homework 8.
  Wednesday, March 31	HW5 rewrite due	4.4 and read the Studyguide.	4.3: 15abcd
  Friday, April 2	HW 7 due		4.4: 2a-e, 5a-f, 6a-f
  Monday, April 5	Rewrite of HW 6 due
  Wednesday, April 7	Midterm Studyguide.
  Friday, April 9	HW 7 rewrite due	4.5	4.5: 1abcd, 2abcd, 3ce
  Monday, April 12				Homework 9. Inductionworksheet. For extra credit on problem 2 of the exam, use this worksheet to give induction proofs of problems 8c, 8b, 8g, 8h, 8t in section 2.4. Every worksheet is worth 3 points extra credit (your maximum amount of points you can get in the problem is 15). So if you got 12 points, you can do one worksheet. If you had 4 points, you can do 4 worksheets. These worksheets are due together with Homework 9.
  Wednesday, April 14	HW 8 due		See Friday's HW -- write them up for practice!
  Friday, April 16
  Monday, April 19		5.1	4.5: 6b	Last Homework.
  Wednesday, April 21	HW 9 due
  Friday, April 23			Check out the Studyguide.
  Monday, April 26
  Wednesday, April 28	Last HW due		Fill out Review questionnaire by Friday. You can select your favorite times for review here.
  Friday, April 30
  Monday, May 3	Final exam, 1:00 - 3:00 PM, MSB 411. Studyguide.