Instructor: Dr. Madnick (jmadnick [at] uoregon [dot] edu)
Office: 1 University Hall
Textbook:
"Understanding Analysis" (2nd Edition) by Stephen Abbott
Here is the e-book (DuckID required)
Lectures: 104 Condon Hall
Mon, Wed, Fri: 12:00 - 12:50
Office Hours: Basement of University Hall
Workshop Problems (optional)
Workshop 1 (Wed 4/12) Solutions
Workshop 2 (Wed 4/26) Solutions
Final Exam Practice. Solutions
Start Here
"Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?" -- Paul Halmos
For fun: Visualizations of infinite series
Review of Calculus 1 (Math 251: Fall '22)
Handouts, Midterm 1, PSets
Midterm 1 Information
Monday 5/1
Time & Location: Our classroom during lecture.
Content:
Lectures 1-9
Relevant assignments: PSets 1, 2, 3.
Unit A. Sections B.1 and B.2.1.
(Although Unit 0 is not the focus of the midterm, everything in Unit 0 will be assumed as basic prerequisite knowledge.)
Structure: Four problems. Maximum score: 38/38.
[8 pts] #1. State definitions and theorems.
[10 pts] #2. Cardinality (A.4). Short response & short proof.
[10 pts] #3. Limits of sequences (B.1 and B.2.1). Two short proofs.
[10 pts] #4. Suprema & Infima (A.1-A.3). One proof.
Time management: Solve problems #1 and #2 quickly. You'll want to have as much time as possible for #3 and #4, which take longer.
Essential tips for studying:
- Memorize all the definitions, propositions, and theorems.
- Go through all the relevant PSets and workshop problems: make sure you can solve all of them.
- The textbook has lots of excellent problems. Consider solving them and/or discussing them with Yongmin or Dr. Madnick.
More tips: For each theorem we've learned:
- Understand why each of the theorem's hypotheses are relevant.
- Reread the proof.
Midterm 2 Information
Wednesday 5/24
Time & Location: Our classroom during lecture.
Content (tentative):
Lectures 9-17
Relevant assignments: PSets 4, 5, 6
Sections B.2-B.6 and C.1.
(Note: Section B.7 won't be tested on this midterm.)
Structure: Four problems. Maximum score: 38/38.
[6 pts] #1. State definitions and theorems.
[9 pts] #2. True/False. Topics: Drawn from B.3, B.4, B.5.
[9 pts] #3. Short response + True/False. Topic: Open sets and closed sets (C.1).
[14 pts] #4. Three short proofs. Topics: Drawn from B.3, B.5, and B.6.
Time management: Solve problems #1, #2, #3 quickly. You'll want to have as much time as possible for #4, which takes longer.
Suggested: Spend 20-25 minutes on #1, 2, 3. Then spend the remaining 25-30 minutes on #4.
Advice:
- Know the reverse triangle inequality. Know what it means for a series to converge.
- Memorize all the definitions, propositions, and theorems.
- Go through all the relevant PSets: make sure you can solve all of them.
- For each theorem we learned: understand why each of the theorem's hypotheses are relevant. Ask whether the converse is true.
- The textbook has lots of excellent problems. Consider solving them and/or discussing them with Yongmin or Dr. Madnick.
Final Exam Information
Thursday 6/15
10:15 am - 12:15 pm
Location: Our classroom.
Content: The final exam is cumulative.
Units C and D make up 75% of the exam, while Units A and B make up the other 25%.
Section C.2 (the Cantor Set) won't be tested.
Section D.5 (Uniform Continuity) won't be tested.
Structure: Nine problems. Maximum score: 78/76.
#1. [10 pts] State definitions and theorems. (Units C and D)
#2. [9 pts] True/False. (Unit C)
#3. [9 pts] Short response/proof (Unit C)
#4. [13 pts] True/False + Short proof (Unit D)
#5. [9 pts] True/False + Short proof (B.6-B.7)
#6. [6 pts] One proof. (B.1-B.2)
#7. [6 pts] One proof. (Unit D)
#8. [8 pts] Two proofs. (Unit D)
#9. [6 pts] One proof. (Unit A and C.1)
Extra credit. [2 pts]
Final Exam Practice Problems
Solutions to practice problems
Advice:
- Work through the final exam practice problems.
- Section D.2 (continuity) will be a significant focus. You should know how to prove that a function is continuous / discontinuous.
- Review the PSet problems. Read the solutions and make sure you can solve the problems on your own .
- Memorize all the definitions, propositions, and theorems.
- For each theorem we learned: ask whether the converse is true. If it's false, you should know a simple counter-example (assuming one exists).