Tiger gotta hunt. Bird gotta fly.
Man gotta sit and wonder why, why, why.
Tiger gotta sleep. Bird gotta land.
Man gotta tell himself he understand.
Kurt Vonnegut Jr.
NOTE: The second exam has been moved to April 13.
- Time and Place. MWF 11:30-12:20 in LART 301
- Instructor. Helmut Knaust, Bell Hall 124, firstname.lastname@example.org, 747-7002
- Office Hours. MWF 10:30-11:20, or by appointment.
- Prerequisites. The course requires a certain level of mathematical maturity that you should have gained by, for instance, having thoroughly and successfully grappled with the concept of infinity in your Calculus II course (which is the formal prerequisite for this course).
- Course Objectives. This is a Foundations course. This means that hardly any prior knowledge is required. The class prepares you "do" mathematics on your own and enables you take more advanced classes or read rigorous mathematical textbooks. You should expect (and I will expect) that you make considerable progress in the following areas:
- Make sense of an abstract definition by analyzing it carefully and constructing examples.
- Make sense of a mathematical statement and be able to bring to bear a variety of strategies for constructing its proof.
- Be able to recognize a rigorous proof when you read one. Conversely, be able to pick out the weak spot(s) in a less rigorous argument. Be able to fill in details in a sketchy proof.
- Once you have devised a proof, be able to write it down in a clear, concise manner using correct English and mathematical grammar.
- Be able to present and defend a proof to a group of your peers.
- Class Participation and Activities. You are expected to always actively participate in class. There will also be some organized in-class activities. Your participation grade will contribute 10% to your grade.
- Homework. I will regularly assign written homework. The graded homework will contribute 20% to your grade.
- Tests. Exams will be given on the following dates: Monday, February 19, and Wednesday, April 13. Each exam counts 20% of your grade.
- Final Examination. The final exam on Wednesday, May 9, 13:00-15:45, is comprehensive and mandatory. It counts 30% of your grade.
- Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.
- Attendance. You are strongly encouraged to attend class. Students with six absences (excused or unexcused) will be dropped from the course with a grade of "F".
- 4/30/07 Program Assessment Test
- 4/27/07 Read 5.2,5.3. Problems: 5.2: 2af,4ab,9,10
- 4/25/07 Read 5.1,5.2.
- 4/23/07 Read 4.4,5.1. Problems: 4.4: 2a-c,3d-f,9a-d,10,11ad,16,20
- 4/20/07 Read 4.4,5.1.
- 4/18/07 Read 4.3,4.4. Problems: 1a-d,2a-d,9a-c,11ab
- 4/16/07 -
- 4/13/07 Test 2
- 4/11/07 -
- 4/9/07 Read 4.1-4.3. Problems: 4.1: 1ab, 3h-j,4a-c,6b,16ab
- 4/6/07 [Good Friday]
- 4/4/07 Read 3.4,4.1,4.2. Problems: 3.4: 11,14b,15,16a,18
- 4/2/07 Read 3.4,4.1.
- 3/30/07 Read 3.4.
- 3/28/07 -
- 3/26/07 Read 3.4. Problems: 3.4: 1c-f,2a,3ade,9
- 3/23/07 Read 3.3-3.4. Problems: 3.3: 2abef,3ade,6cd,8,11
- 3/21/07 Read 3.2,3.3. Problems: 3.2: 4fgh,6ab,7a-c,8,10-13
- 3/19/07 Read 3.2,3.3. Problems: 3.2: 1abckl,2a-c,3a-c,4fgh
- 3/9/07 Groups 5 and 6 prepare for In-Class Activity 3.
- 3/5/07 Read 3.1,3.2. Problems: 3.1: 13,16,18; prepare for In-class Activity 3
- 3/5/07 Read 3.1,3.2. Problems: 3.1: 5cd,10ijp,11c
- 3/2/07 Read 3.1,3.2. Problems: 3.1: 3f,4a,5ab,6
- 2/28/07 Read 2.5, 3.1.-3.2. Problems: 2.5: 2,3a,7
- 2/26/07 Read 2.4-3.1.
- 2/23/07 Read 2.3-2.5.
- 2/21/07 Read 2.3-2.5. Problems: 2.3: 1abj,10a,11,13,15
- 2/19/07 Test 1
- 2/16/07 Read 2.3-2.5. Problems: 2.4: 8 abcors
- 2/14/07 Read 2.2-2.4. Problems: 2.2: 2,4b,10ab,14d-f
- 2/12/07 Read 2.1-2.3. Problems: 2.1: 3,7d-f,10a,14,17
- 2/9/07 -
- 2/7/07 Read 1.6,2.1,2.2. Problems: 1.6: 1gj,2ac,6
- 2/5/07 Read 1.5,1.6,2.1. Problems: 1.5: 3aef,4b,5a,12ab
- 2/2/07 Read 1.4-1.6. Problems: 1.4: 5bc,6c,7g,11a
- 1/31/07 Read 1.3-1.5. Problems: 1.3: 1a-e,2a-e,5a-d,8ab,12
- 1/29/07 Read 1.3-1.4.
- 1/26/07 Read 1.3-1.4. Problems: 1.2: 1b-e,2b-e,4a-c,6cf,9a
- 1/24/07 Read 1.1-1.3. Problems: 1.1: 2cej,4ef,5ad,10a-c
- Information about LaTeX
- In-class Activity 3 Pictures Mathematica notebook
- The square root of 2 is irrational, again.
- Induction Principles
- Polya's "How to Solve It"
- How to Check Proofs
- In-class Activity 2
- In-class Activity 1
- A simple proof that π is irrational (by Ivan Niven)
- Communicating Mathematics through Homework
- Short History of Proof