MATH 312, Concepts of real analysis (An introduction to rigorous analytic proofs involving properties of real numbers, continuity, differentiation, integration, and infinite sequences and series.)

Syllabus - Extra credit problems

• HWA1, due Wen, Jan. 18.
  • Read and understand: 1.1;
  • Read: 1.2;
  • Exercises: 1.1.3, 1.1.4, 1.1.8, 1.1.10, 1.2.5.
• HWA2, due Mon, Jan. 23.
  • Read and understand: 0.3.1--0.3.2 and 1.2;
  • Read: 1.3--1.4;
  • Exercises: 0.3.11, 1.1.5, 1.2.2, 1.2.12.
• HWA3, due Mon, Jan. 30.
  • Read and understand: 1.3;
  • Read: 1.4, 2.1;
  • Exercises: 1.1.9, 1.2.8, 1.2.9, 1.3.1, 1.3.3.
• HWA4, due Mon, Feb. 6.
  • Read and understand: 1.4;
  • Read: 2.1;
  • Exercises: 1.2.10, 1.3.2(a), 1.4.4, 1.4.6(a), 1.4.7.
• HWA5, due Mon, Feb. 13.
  • Read: 2.1, 2.2;
  • Exercises: 2.1.7, 2.1.15, 2.1.17, 2.2.5, 2.1.20.
• HWA6, due Mon, Feb. 20.
  • Read and understand: 2.1, 2.2 and Solutions of quizzes;
  • Read: 2.3;
  • Exercises: 2.1.13, 2.1.22, 2.2.6, 2.2.12(a), 2.3.7
• Midterm in class, Fri. Feb 24, five problems:
  • two problems from the HWA's or Quizzes;
  • two theorems or its parts from the following list (the choice is mine):
    0.3.24, 1.1.8, 1.1.9, 1.2.2, 1.2.4, 1.2.5, 1.2.7, 1.3.1, 1.3.2, 1.3.3, 1.4.1,
    2.1.6, 2.1.7, 2.1.10, 2.1.17, 2.2.1, 2.2.3, 2.2.5, 2.3.2, 2.3.4, 2.3.5.
  • one new problem.
• HWA7, due Mon, Mar. 13.
  • Read and understand: 2.3.
  • Read: 2.4;
  • Exercises: 2.3.1, 2.3.5(b), 2.3.6, 2.3.11, 2.3.12
• HWA8, due Mon, Mar. 20.
  • Read and understand: 2.4,
  • Read: 2.5;
  • Exercises: 2.4.2, 2.4.6, 2.4.8, 2.5.2, 2.5.4
• HWA9, due Mon, Mar. 27.
  • Read and understand: 2.5, 2.6.2
  • Read: 3.2;
  • Exercises: 2.5.3(a,e), 2.5.6(a), 2.6.1(b,c), 3.2.10, 3.2.15.
• HWA10, due Mon, Apr. 3.
  • Read and understand: 3.2, 3.3
  • Read: 3.6;
  • Exercises: 3.2.14, 3.3.2, 3.3.3, 3.3.6, 3.6.8.
• HWA11, due Mon, Apr. 10.
  • Read and understand: 4.1, 4.2
  • Read: 4.4;
  • Exercises: 4.1.5, 4.1.11, 4.2.4, 4.2.5, 4.2.8.
• HWA12, due Mon, Apr. 17.
  • Read and understand: 5.1, 5.2
  • Read: 5.3;
  • Exercises: 5.1.1, 5.1.2, 5.1.9, 5.2.4, 5.2.14(a)
• HWA13, due Mon. Apr. 24.
  • Read and understand: 5.3, 5.4
  • Exercises: 5.2.16, 5.3.3, 5.3.5, 5.3.8, 5.4.6(a)
• Final exam, Mon. May 1, 8:00--9:50 Forum Bldg 108
  • three problems from the HWA's;
  • three theorems or its parts from the following list (the choice is mine, you might be asked to give a retated definition):
    1.2.4(i,ii), 1.2.7,
    1.3.2, 1.3.3,
    1.4.1,
    2.1.6, 2.1.7, 2.1.10,
    2.2.1,
    2.3.4, 2.3.8,
    2.4.4, 2.4.5,
    2.6.2,
    3.2.7,
    3.3.1, 3.3.2, 3.3.7,
    3.4.4,
    3.6.4,
    4.2.3,
    5.2.6,
    5.3.1,
    5.4.1.
  • two new problems.
• Sample exam:
  • Theorems: 1.4.1 (+def. of countable set), 2.1.6 (+def. of converging sequence), 5.3.1;
  • Exercises: 3.2.15, 4.1.11, 5.4.6,
  • New problems: 2.4.4, 2.5.3(b),