Triet M. Le
Email:
Phone: (203) 432-4011
Office: Dunham Lab. 418

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Math 301/ENAS 513: Introduction to Analysis, Fall 2007
Time: Tuesday and Thursday, 1:00-2:15
Location: LOM 214
Text: "Analysis: An introduction" by Richard Beals
Office Hours: Tuesday, 4:00-5:00, and Wednesday, 5:00-6:00

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The course will cover most of chapters 1 -9 in the book. Three theorems will be of special interest: the Bolzano-Weierstrass Theorem; the Contraction Mapping Theorem; and the Weierstrass Approximation Theorem. It is expected that students will be fully familiar with proofs and some applications of these theorems.

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Prerequisites: In addition to those listed in the course catalogue, basic knowledge of real and complex numbers (including polar form) is assumed. It is also assumed that students have basic knowledge of geometric series and the integral test (page 52). Sections 1A and 1B will be covered very rapidly in class, so be sure to carefully read these sections.

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Homework: There will be weekly homework assignments, due in class on Thursdays. No late homework will be accepted.

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Exams: There will be a midterm and a final exam. The Midterm is on Thursday, 10/25/2007, from 6-7:30pm in LOM 214.

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Grading: The grading scheme is: 30% for the midterm; 40% for the final; 30% for homework.

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Reading and Homework assignments: The pages listed for each week contain the topics to be discussed in class that week. The problems listed in "Homework" are due in class on the Thursday of the week they are listed in. (So there is no homework due the first week of class, and the first homework is due on Thursday, Sept. 13.) If an assigned problem has several parts (i.e. a,b,c,d,e) and no specification is given, you are to solve all parts.

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Warning: Some of the book's hints for solutions are either very hard to understand or listed for the wrong problem! If in doubt about a hint, ask!

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Annoucements:

• (09/08/2007). There are typos in the text. Here are the corrections provided by Professor Richard Beals.
• (09/11/2007). The problems from section 2A (page 20) are excluded from homework 1; for I did not go over that section today. Please see the link below for an updated version of hw1.pdf.
• (10/10/2007). Only need to turn in the first three problems in hw5.pdf.

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Week 1: Sept. 3-7, 2007

• Reading: Up to page 14.
• Practice Problems (Do not hand in):
• Page 5: 1, 2, 3, 4, 5
• Page 9: 1, 5, 14

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Week 2: Sept. 10-14, 2007

• Reading: Up to page 28.
• Homework: hw1.pdf.

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Week 3: Sept. 17-21, 2007

• Reading: Up to page 35.
• Homework: hw2.pdf.

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Week 4: Sept. 24-28, 2007

• Reading: Up to page 47.
• Homework: hw3.pdf.

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Week 5: Oct. 1-5, 2007

• Reading: Up to page 57.
• Homework:
  • Page 44: 7, 10;
  • Page 48: 1, 2, 3;
  • Page 53: 2, 6, 13, 20;

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Week 6: Oct. 8-12, 2007

• Reading: Up to page 72.
• Homework: hw5.pdf.
  • Notes: Only need to turn in the first three problems in hw5.pdf.

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Week 7: Oct. 15-19, 2007

• Reading: Up to page 85.
• Homework: hw6.pdf.
• The Midterm Exam (10/25/07) covers materials from the text book upto page 72, excluding sections 2C and 4D.

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Week 8: Oct. 22-26, 2007

• Reading: Up to page 88.
• Homework: Due Tuesday, 10/30/2007.
  • Page 74: 1, 2;
  • Page 78: 5, 8, 10;
  • Page 81: 1;
  • Page 83: 4, 7, 12;
• The Midterm Exam (10/25/07) covers materials from the text book upto page 72, excluding sections 2C and 4D.

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Week 9: Oct. 29-Nov. 2, 2007

• Reading: Up to page 95.
• Homework: hw8.pdf.
• Midterm Solution: mid_soln.pdf.

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Week 10: Nov. 5-9, 2007

• Reading: Up to page 104.
• Homework:
  • Page 89: 8, 10, 11, 13, 15.
  • Page 91: 3, 6.
  • Page 94: 2, 3, 6.

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Week 11: Nov. 12-16, 2007

• Reading: Up to page 112.
• Homework:
  • Page 104: 1(a,c,f), 2, 3, 4b, 6.

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Week 12: Nov. 26-30, 2007

• Reading: Up to page 116.
• Homework:
  • Page 107: 3(a,b), 5;
  • Page 112: 1, 2, 3, 5, 6;

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Week 13: Dec. 3-7, 2007

• Reading: Up to page 130.
• Homework:
  • Page 116: 2, 3;
  • Page 117: 2,3, 4, 5, 6, 8, 11;
  • Page 123: 1, 3, 5(a,b,c), 7;

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Reading Week: Dec. 10-14, 2007

• Office Hours: Tue. & Thur.: 1-2:15pm. Wed.: 4-6pm.

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• The final is on Thursday, December 20, 2007 from 2:00 PM - 5:30 PM in LOM 214.
• It will cover materials from the textbook up to page 116, excluding sections: 2C, 4D, 5D, and 7D.
• There will be 10 questions.
• Pay special attentions to the Bolzano-Weierstrass Theorem; the Contraction Mapping Theorem; and the Weierstrass Approximation Theorem.
• Here is a sample of practiced questions for the final.

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