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Math 414 Problems, Comments

Math 414 Problems, Comments 
Spring 2020

I'll put comments- assignments, things missed in class, etc. on this link. Probably you should check a couple times each week to see if anything is added.

week 1 :
Practice problems (PP's) for Friday Jan. 24: 1) Why is 0<1? 2) Let S be the set of all rationals except 7. Is S an ordered field? Is S an ordered set?

Sec. 1.1 probs: 1,3,5; Sec. 1.2 probs: 1,2,5,8; Sec. 1.3 probs: 1, 3.

HW 1 (Due Monday Jan 27: problems 1.1.4 (3 inequalities to prove), 1.1.8a, 1.1.12, 1.2.9 (Supremum part only), 1.2.15a
 

   
week 2 (Jan 22, 24):  

Reminder: HW is due Monday the 27th

 

   
week 3 (Jan 27 to 31):  
PP's (Practice problems) for Friday: 2.1: 1,2,3,5,6,14; 2.2: 5,7

There will be a Quiz Friday after PP's. Also, here is HW2 , (Due 2-7)

   
week 4 (Feb 3 to 7):  
PP's for next Wednesday: 2.2: 2; 2.3: 5a, 5b, 7a, 7c. I'll add some more later. Check back.

Hints on some HW prob's: for 1b, try to find a number B so that x_n < B / n for all n. (THen base your M on this inequality.) For 2a, it might be best to apply the Squeeze lemma to a tail of the sequence for which the sequence is bounded above and below by sequences of the form C/n.

Here are some practice exam problems Practice Exam 1 You can include these with the practice problems for Wednesday next week.

   
week 5 (Feb 10 to 14):  
Here are some solutions to HW 1 (This should work fine- refresh your browser (if this does not give the HW solutions).

Here are some solutions to HW 2

   
week 6 (Feb 17 to 21):  
Test 1 was worth 40 points.

Curve for Test 1: 34-40 A; 28-33 B; 21-27 C; 14-20 D.

   
week 7 (Feb 24 to 28):  
HW 3 (Due Monday March 2): 2.4: 4; 2.5: 3b,c,d, 4a, 9a; 2.6: 1c,d, 5c,e

PP's for Friday Feb 28: 2.4: 1; 2.5: 3a,e, 4b, 9b, 2.6: 1a,b, 5a,b,f; 13

   
week 8 (March 2 to 6):  
PP's for Friday March 6: 3.1: 1 a,b,c,d,e; 5, 8; 3.2: 4, 9, 12
 
   
week 9 (March 9 to 13):  
HW 4 (Due Monday March 23) 3.1: 2, 13; 3.2: 2,3,10; 3.3: 3, 7, 12

 

PP's for Friday March 13: 3.2: 5 (consider a sequence going to 0), 12 (consider delta=12), 14(consider left and right limits); 3.3: 1,2,3, 10, 11, 14, 3.4: 4

Our class for Monday March 23 will be an online class. HW 4 is due at the beginning of that class. Options to turn in the HW are 1) put it under my door (494 Carver) anytime before class; 2) make a high quality .pdf file of your homework by scanning it and email it to me. If you email it, it should be in 1 file not many separate files. I would greatly prefer you do NOT send screenshots of your HW since those usually come in separate files and often are difficult to read.

 

Since several people could not attend class the week before Spring break, I rewrote some of the lecture notes sections 3.2, 3.3 and part of 3.4