MAA 6406/07 Suggested Problems
Exercises 12.4.1, 12.4.2. Show sin(z)=z has infinitely many solutions; show f(z)=exp(z)-z takes every value infinitely often. [22 March]
Exercises 10.3.1, 10.3.7. [24 Feb]
Exercises 10.2.1, 10.2.5, 10.2.7. [15 Feb]
Exercises 10.1. 10.7, 10.8. 10.9, 10.11. [10 Feb]
Exercises Read 8.1.1, 8.1.3, do 8.2.2, 8.2.4. [6 Feb]
Exercises 7.8.5. [30 Jan]
Exercises 7.8.2, 7.8.3, 7.8.4. [27 Jan]
Exercises 7.7.1, 7.7.2, 7.7.3, 7.7.5, 7.7.8. [25 Jan]
Exercise 7.6.1. [23 Jan]
Exercises 7.5.12, 7.5.13 in both cases ignoring the {most elementary}. [20 Jan]
Exercises 7.5.1, 7.5.6, 7.5.6, 7.5.7, 7.5.8 (prod (1-z^n) only). [18 Jan]
Exercises 7.4.1, 7.4.2, 7.4.5, 7.4.9. [7 Dec]
Exercises 7.2.1, 7.2.4, 7.2.6, 7.2.8, 7.2.10, 7.2.11, 7.2.13. [2 Dec]
Exercises 7.1.7. [28 Nov]
Exercises 7.1.2; 7.1.5, 7.1.8. [21 Nov]
Exercises 6.2.2, 6.2.3, 6.2.6. [16 Nov]
Exercises 6.1.1, 6.1.2, 6.1.3(but don’t take part c to seriously); 6.1.4, 6.1.6, 6.1.7. [16 Nov]
Exercises 5.2.1(a,b,d); 5.2.2(a,e); 5.2.7, 5.2.12, 5.3.3, 5.3.5, 5.3.9. [14 Nov]
Exercises 5.1.1, 5.1.4(a); 5.1.14, 5.1.15. [7 Nov]
Exercises 5.1.6, 5.1.7, 5.1.8, 5.1.9, 5.1.10. [4 Nov]
Exercises 4.7.2, 4.7.4, 4.7.7. [28 Oct]
Exercises 4.6.4, 4.6.5, 4.6.6, 4.6.8, 4.6.9 and use the result and Theorem 5.6 from chapter IV in Conway to prove Theorem 6.7 in Chapter IV in Conway (under the obvious additional hypotheses). [26 Oct]
Exercises 4.5.3, 4.5.5, 4.5.7, 4.5.8, 4.5.9, 4.5.10. [24 Oct]
Exercises 4.4.3, 4.4.4. [19 Oct]
Exercises 4.5.8, 4.5.9. [17 Oct]
Exercises 4.3.3, 4.3.4, 4.3.5, 4.3.6, 4.3.8. 4.3.9, 4.3.10 (Hint: All have very short proofs). [14 Oct]
Exercises 4.3.2, 4.3.6. [12 Oct]
Exercises 4.2.2, 4.2.3, 4.2.5, 4.2.7(a,b); 4.2.9(a,c); 4.2.11. [10 Oct]
Exercises 4.1.11, 4.1.12, 4.1.13, 4.1.20, 4.1.21. [3 Oct]
Exercises 3.3.8, 3.3.14, 3.3.16, 3.3.13 (yes out of order); 3.3.17. [26 Sep]
Exercises 3.3.1, 3.3.2, 3.3.8(read); 3.3.26. [23 Sep]
Exercises Determine the images of lines parallel to the real and imaginary axes under cos. [Suggestion, apply Exercise 3.2.7 to cos(x+iy).] Exercise 3.3.4. [19 Sep]
Exercises 3.2.11, 3.2.19. [16 Sep]
Exercises 3.2.6, 3.2.7, 3.2.15. [14 Sep]
Exercises 3.1.6, 3.1.7. [12 Sep]
Exercise 2.5.9 [31 Aug]
Exercise 2.2.3 (no proofs). [29 Aug]
Exercises 2.1.7, 2.1.11 (note that the set of points k mod 2pi (for natural numbers k) is an infinite set. Hence any non-trivial subinterval of [0,2pi) contains two such points. Now use the group structure of the unit circle (equal reals mod 2pi.] . [26 Aug]
Exercises 1.3.3 (Section 1.3 problem 3); 1.4.2 (c); 1.4.5, 1.4.6. [24 Aug]