HOMEWORK

Problems listed here need to be solved, written up and submitted for grading each Wednesday.
However, you are encouraged to solve more problems, and to try to prove statements proved in class all by yourself. The more problems you solve, the better you become, this is how you learn math! 

To be submitted on W Aug 29:
W Aug. 22: Sec.1.1: solve 2, 3,10, 14, 15 for unions (intersections did in class), 16 and find the inverse function.
F Aug. 24: Sec.1.1 solve 19. Sec.1.2 solve 5, 6, 10, 11 (conjecture and prove by induction, OR use Example a to calculate), 16, 20
M Aug. 27: Sec.1.3 solve 1, 2, 4, 12 (I moved problem 9 for the next HW set)
To be submitted on W Sept 5:
W Aug. 29: Sec.1.3 solve 9, 6, 7
F Aug. 31: Sec. 2.1 solve 1; Sec. 2.5 solve 16, 17
Hand-out: Real numbers (revised)
M Sept. 3 Labor Day! no classes
W Sept. 5: Sec.2.2: 5, 6b, 7, 9, 10, 13
                 Use mathematical induction to show that |a_1+...+a_n|<=|a_1|+...+|a_n|
F Sept. 7: Review. Here are some review problems and solutions.
To be submitted on W Sept 19:
W Sept. 12: Sec.2.2: 16, 17 These are super-important properties of neighborhoods! Remember them and use them later.
                    Sec.2.3: 2 (with proofs), 4, 5a, 8
F Sept. 14: Sec.2.3: 10, 11
                    Sec.2.4: 4, 6, 7, 8, 9
M Sept. 17: Sec.2.5: 2, 3, 8, 10
To be submitted on W Sept 26:
W Sept. 19: Sec.3.1:  5a,d, 6c, 7, 8. Also, do not submit, but definitely solve 2, 3,4.
F Sept. 21: Sec.3.2:  6, 7, 10a, 11, 12
M Sept. 24: Sec.3.2:  16, 18, 19, 20
To be submitted on W Oct. 3:
W Sept. 26: Sec. 3.3: 2, 3, 7, 9 (useful fact, to be remembered!)
F Sept. 28: Sec.3.4: 4b, 7, 10 (useful fact, to be remembered!)
M Oct. 1st: Sec.3.5: 4, 5, 9, 11 (you can use the form of solutions of such recurrences as discussed in class)
To be submitted on W Oct. 10th (the day of the second midterm!)
W Oct. 3: Sec.3.5: 13, 14. Sec.3.6: 1, (think but do not submit #2), 4b, 6, (know to prove but do not submit #7,#9), 8
F Oct. 5: Sec. 3.7  2, 3bc, 4, 5, 6a, 7, 11, 12. Read 15 but do not prove it, use it in 16 to establish the nature of the p-series.
M Oct. 8: Review problems. Also solve from Sec 3.6 the problems 1, 6b.  Solutions to the review problems.
W Oct. 10: Midterm exam. Homework is due.
    Enjoy!
To be submitted not this W, but on W Oct. 24
M Oct. 15:  Sec. 4.1: 1bc, 3, 4, 6, 9b, 13, 16, 17
W Oct. 17:  Sec. 4.1: 12bcd, 15
F Oct. 18:  Sec. 4.2: 1c, 2, 3, 4, 5, 9. Solve but do not submit for grading:11, 14
M Oct. 22:  Sec. 4.3: 4, 5bdh, 6, 7, 9. Solve and remember for future use but do not submit: 8. All the exercises in 4.3 are interesting! Solve as many as you can.
To be submitted on W Oct. 31st  
W Oct. 24:  Sec. 4.3: 2, 3, 5acefg, 8, 11
                      Sec. 4.2: 13
F Oct. 26:  Solve the problems here. Here are some hints.
M Oct. 29:  Sec. 5.1: 1, 2, 3, 4abd, 5
To be submitted on W Nov. 7
W Oct. 31:  Sec. 5.1: 6, 8, 10, 11, 12, 13
                      Sec. 5.2: 3
F Nov 2nd:  Sec. 5.2: 1c, 4, 7, 8, 10, 12, 13, 14
M Nov 5th:  Sec. 5.3: 1, 2, 3
To be submitted on W Nov. 14
W Nov. 7th:  Sec. 5.3: 4, 6, 7 (do not use calculator, use only x=Pi/6, Pi/4, Pi/3 to narrow the interval), 13
F Nov. 9th:  Sec. 5.3: 14, 15, 17
                      Sec. 5.4: 1, 3a, 5, 6
M Nov. 12: Office hour 2-3PM
To be submitted after Thanksgiving, on W Nov. 28
W Nov. 14th:  Sec. 5.4: from 7 show only that f(x)=x and g(x)=sin(x) are uniformly continuous on R, 8, 9, 10
                  Which of the following are uniformly continuous: a) f(x)=x^3 on [0,1], b) f(x)=x^3 on (0,1), c)f(x)=x^3 on R, d) sin(1/x^2) on (0,1),  e)   x sin(1/x^2) on (0,1).  
 F Nov. 16th:  Sec. 5.4:  (the first 3 problems help build intuition:)12, 13, 14, 15, 16
M Nov. 19: Sec. 5.6: 1, 2, 3, 4, 5, 6, 7 
Welcome back!               
M Nov. 26th: Sec. 5.4: 10(important property!), Sec 5.6: 8, 9
To be submitted on W Dec 5th (last day of class)
W Nov. 28:  Sec. 5.6: 10, 11, 12
                   Show that the exponential function defined by its Taylor series is continuous at x=0, then deduce it is continuous on R.
                    IVT but with limits: Let f:R->R be continuous, such that lim f(x) when x->infinity equals infinity and lim f(x) when x->-infinity equals 0. Show that f takes any value in (0,infinity)
------Only one problem will be graded, for a max of 5 points.
F Nov. 30th: Approximation! (from Sec. 5.4) Homework: please complete the evaluation of instruction!
Review materials: Topics and problems.   Solutions to some problems.
M Dec 3rd: Sec. 5.5 (optional here, but needed in the next semester, Math 4548)
W Dec 5th: Review More Review Questions   Steps towards solutions (you may need to explain more)
Final exam: according to university schedule, found here.
Namely, the section meeting at 12:40 will have the final on Thursday Dec 13, 2PM-3:45PM
and the section meeting at 3PM will have the final on Friday Dec 7,   12:00pm-1:45pm.
(Please check this info and correct me if it is not correct.)