MATH 301, Introduction to Mathematical Analysis I, Fall 2009

Course Information

• Lectures: Mon and Wed, 5:10-7:00 pm, SOND 206
• Textbook: Introduction to Real Analysis, 3rd Edition, John Wiley and Sons, Inc.
• Office Hours: Mon and Wed, 4:00-5:00 pm
  
• Syllabus
  
• UMBC Academic Integrity Statement
  

Exams

• Exam II will be given on Nov. 11 (Wed) in class. It covers Sections 3.1-3.6.
• Exam I will be given on Oct. 19 (Mon) in class. It covers Sections 1.1-1.3 and 2.1-2.4.

Quizzes

• Quiz III will be given on Dec. 2 (Wed) in class. It covers Sections 4.1-4.2 and 5.1.
• Quiz II will be given on Nov. 2 (Mon) in class. It covers Sections 3.1-3.3.
• Quiz I will be given on Sept. 28 (Mon) in class. It covers Sections 1.1-1.3.

Homework

• Hw #11, due Nov. 30 (Mon)

  • Sec. 5.2, p.128: 1(a), 3, 5, 6, 8(hint: think of 12 of Section 5.1), 11;
    
  • Suggested reading : Section 5.3
    

• Hw #10, due Nov. 23 (Mon)

  • Sec. 4.2, p.110: 1(c), 2(b), 4, 5, 10;
    
  • Sec. 5.1, p.124: 6, 9, 10, 12(hint: use the Density Theorem), 13;
    
  • Suggested readings : Sections 5.1, 5.2
    

• Hw #9, due Nov. 16 (Mon)

  • Sec. 4.1, p.104: 1(c), 3, 9(b,c), 11, 12, 14(hint: use the Density Theorems for (b));
    
  • Suggested readings : Sections 4.1, 4.2
    

• Hw #8, due Nov. 4 (Wed)

  • Sec. 3.5, p.86: 2(a), 4, 7, 9, 10, 12(hint: prove by induction that x_n is positive for all n first and then show that the sequence is contractive);
    
  • Sec. 3.6, p.88: 2, 9, 10(hint: in order to use Theorem 3.6.5 or alike, show that there exists a natural number m s.t. a_n>0 for all n >= m);
    
  • Suggested readings : Sections 3.6, 4.1
    

• Hw #7, due Oct. 28 (Wed)

  • Sec. 3.2, p.68: 21;
    
  • Sec. 3.3, p.74: 2, 7, 8: show the existence of lim(a_n), lim(b_n) and lim(a_n)<=lim(b_n), 9, 10: show that (t_n) is monotone and convergent and that if lim(s_n)=lim(t_n), then (x_n) is convergent (hint for the latter claim: use the squeeze theorem);
    
  • Sec. 3.4, p.80: 4, 5, 9, 11, 12, 16;
    
  • Suggested readings : Sections 3.3-3.5
    

• Hw #6, due Oct. 21 (Wed)

  • Sec. 3.1, p.60: 5(a, b, d), 8, 10, 17;
    
  • Sec. 3.2, p.67: 1(b, d), 2, 4, 7; (you are allowed to use limit theorems of this section whenever necessary)
    
  • Suggested readings : Sections 3.1-3.2
    

• Hw #5, due Oct. 14 (Wed)

  • Sec. 2.3, p.38: 2, 3, 5, 8, 10: prove inf S <= inf S_0 only;
    
  • Sec. 2.4, p.43: 3, 4(a), 6: prove sup(A+B)=sup A+sup B only, 18;
  • Suggested readings : Section 2.4
    

• Hw #4, due Oct. 5 (Mon)

  • Sec. 2.1, p.29: 8 (hint for 8: you may use the fact that the sum and product of two integers remain integers), 11(b), 13, 14, 16(c, d), 18;
    
  • Sec. 2.2, p.34: 2, 4, 5, 8(b), 15;
  • Suggested readings : Sections 2.3, 2.4
    

• Hw #3, due Sept. 28 (Mon)

  • Prove that a nonempty set T1 is finite if and only if there exist a finite set T2 and a bijection f such that f:T1->T2.
  • Prove that a nonempty set T1 is denumerable if and only if there exist a denumerable set T2 and a bijection f such that f:T1->T2.
    (hint for the above two problems: use Problem 19 of Section 1.1 and the fact that if f:A->B is a bijection, then its inverse function from B onto A is also a bijection)
  • Sec. 1.3, p.21: 4;
    
  • Sec. 2.1, p.29: 1(b), 2(b,d), 4, 5;
    
  • Suggested readings : Sections 2.1, 2.2
    

• Hw #2, due Sept. 21 (Mon)

  • Sec. 1.1, p.11: 9, 12, 14, 17(a), 19, 20(b);
    
  • Sec. 1.2, p.15: 5, 7, 14;
    
  • Suggested readings : Sections 1.3, 2.1
    

• Hw #1, due Sept. 14 (Mon)

  • Use the truth table to prove the 2nd DeMorgan's Law on p.336 of Appendix A;
    
  • Use the truth table to prove: (P=>Q) is logically equivalent to [(not P) or Q];
    
  • Sec. 1.1, p.11: 1, 3, 5;
    
  • Suggested readings : Appendix A, and Sections 1.1
    

Copyright © Jinglai Shen
Last updated, August 2009