Advanced Calculus
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Professor: Thomas Schlumprecht
Office: Milner 118
Officehours: Mo 3:00 - 4:00 Thu 3:00- 4:00 or by appointment
Email: schlump@math.tamu.edu
Use in your proofs only the axioms, facts proven in class, facts
proven in the text, or facts you proved previously.
Page 11 1,3,6(a),11
Page 17 1(b), 6(b)
Page 23 1 (in that problem only write down the answer without proof)
Page 23 2, 3, 6, 9, 10
Show for two bounded (bounded below and bounded above) subsets A and B of the real line:
sup(A-B)=sup(A)-inf(B)
Page 33 1(a),(b),(c) 4(a),(b),(c)
Page 33 3, 6, 7,8(only iv and v),9 , 10
Show that the set of all finite subsets of N is countable.
Show that the set of all infinite sequences consisting of 1 or 0 is
uncountable (Cantor's diagonalization!) and deduce from it that the
set of all subsets of N is uncountable.
Page 38 1(a)(c), 2(a)(c), 4, 5 (Please note that for these problems you should not
use the limit theorems of the next section)
Page 43 1(a)(c), 3, 6 (extended numbers means that they could be + or - infinity)
Test 1, on Wednesday 09/24, What you need to know
Page 51 1, 4, 5, 8
Page 55 1(b)(c), 2, 4
Page 63/64 1(a),(b) 2(a) 3(c),(e)
Prove first part of Theorem 3.8 (about sums) only
using the definition of limits (and not the sequential description)
Page 69 5 (use trig-identities), 7
Page 78 1(b)(c), 2(b)(c),(e), 3, 6, 7, 10
Test 2, on Wednesday 11/05 (rescheduled), What you need to know
Page 83 1(c) 2(d) 4
Page 114 1(a) (b) 2(a)(b)c)
Page 126 1 (a)(b) 2 4 5 8
Test 3, on Monday 11/25, What you need to know