MATH 347 E1H: Fundamental Mathematics (Honors Section)
Spring 2012
Professor A.J. Hildebrand
http://www.math.illinois.edu/~hildebr/347/

Course Policies, Exams, Grades

• Course Information Sheet. General course information: Everything you need to know about this course: Instructor contact, text and syllabus, exam and homework information, grading policies, etc.
• Exams:
  • Sample exams. Links to sample exams from past Math 347 Honors classes. These should give you a good idea of what to expect.
  • Midterm Exam 1: Feb. 15
    • Exam 1 Information.
  • Midterm Exam 2: March 7 (tentative)
  • Midterm Exam 3: April 18 (tentative)
• Final Exam: Wednesday, May 9, 8:00 am - 11:00 am. This is the official Final Exam slot for classes meeting MTWR 12 pm. Please keep this date in mind when making travel plans.
• Add/drop deadlines: January 30 and March 9. The first date (January 30) is the last date you can add a course; if you want to switch to a non-honors section, you have to do so by that date since a section switch involves dropping one course and adding another. The second date (March 9) is the campus deadline for dropping a course. Engineering students need to get their Dean's approval if they drop a course after the 10th day of class.

Announcements

• Open House Hours: Tentatively scheduled for Tuesdays/Thursdays, beginning at around 5:15 pm, and Sundays, beginning at around 3 pm, in 159 Altgeld, beginning the second week of class. The Open House is an informal office hour and get-together for students in my classes, and the primary point of contact for my students. I will stay as long as necessary - typically at least an hour, and sometimes much longer. I will add a third Open House hour if there is enough interest. The Open House room, 159 Altgeld, is a small classroom located in the basement of Altgeld Hall on the south side of the building. We have exclusive use of this room during the above Open House hours.
• Illinois Geometry Lab (IGL). The IGL is a recently established center that provides an opportunity for undergraduates to participate in research projects. For more information, click on the above link, email igl@math.uiuc.edu, or visit the IGL open house on January 17, 5 pm, in 102 Altgeld Hall.

Handouts

Solutions to worksheet problems will be posted here within about a week of handing out the worksheet.

Solutions to homework assignments will be distributed in class at the time the assignment is returned, but will not be posted here in order to comply with departmental policies. If you are missing a solution set, you can pick up an extra copy at my office.

• Induction Proofs, I: Basic Examples.
  Solutions.
• Sum/Product Notation.
  Solutions.
• Logical statements: Terminology and notation.
• Worksheet: Logical statements.
  Expanded version, with space for doing the problems.
  Solutions.
• Worksheet: Even/odd Proofs.
  Solutions.
• Set-theoretic notation and terminology.
  Solutions.
• HW Assignments: HW 1. HW 2. HW 3.
  Honors HW 1.

Class Diary

• Friday, 2/10:
  • Class. Strong induction. Recurrences and Fibonacci numbers. (This material will not be on the exam, but will be the subject of the next HW assignment.)
• Wednesday, 2/8:
  • Class. Induction proofs, continued.
• Monday, 2/6:
  • Class: Started Chapter 3. Overview of types of induction proofs. The Induction Principle, and why it "works". Intuition: Row of dominos tipping over. Handout out worksheets on sum/product notation and induction proofs.
  • Read/do: Read the first few pages of Chapter 3 (through the discussion of summation notation on pp. 53/54). Work through some of the induction problems on the Induction worksheet, using the sample induction proof as model. Also, do the problems on the Sum/Product Notation worksheet.
• Friday, 2/3:
  • Class: Finished the discussion of logical statements. The significance of the order of quantifies. How to analyze, and work with, more complex logical statements such as those in the last problem of the Logic Worksheet.
  • Homework 3: HW 3, due Friday, 2/10. The assignment consists of the following induction problems from Chapter 3: 15, 22, 28, 29, 31, 32, 43, 49(b). (We will start Chapter 3 next week. I will pass out the official coversheet in Monday's class, as well as a handout with sample induction proofs that you can use as models and templates for the homework.)
• Wednesday, 2/1:
  • Class: Conditionals. Implications, converses, contraposition. Practice with mathematical definitions: Increasing versus nonincreasing versus "not increasing".
  • Do: If you have not done so, work through the problems on the Logic Worksheet. (Note that solutions are now posted; see the above link.) Problems 1 and 2 should be completely routine by now, and you should have little difficulty with Problems 3 and 4 (negations of mathematical definitions). In Friday's class, we will focus on more complex manipulations of mathematical statements such as those in Problem 5.
  • Homework: Honors HW 1.
• Monday, 1/30:
  • Class: Logical statements, quantifiers, negations.
  • Read/do: Read pp. 27 - 34 in the text. Familiarize yourself with the basic logical concepts, notations, and terminology summarized on the Logic Handout. Also, start working problems from the Logic Worksheet, and the problems from Chapter 2 on this week's HW assignment.
• Friday, 1/27:
  • Class: Finished the "Even/odd proofs" worksheet with some examples of proofs by contradiction; in particular, gave a proof of the irrationality of squareroot of 2. Handed out new worksheet on logical statemenets (see above for links). This material corresponds to Chapter 2 of the book. We will begin working on these problems next week.
  • Homework: HW 2, due Friday, 2/3.
  • Read/do: Get started on the new assignment (HW 2). The first few problems are of the same type as the "even/odd" problems from this week's worksheet. The remaining problems are logic exercises from Chapter 2. If you want to get a headstart, read up on this material in the book and started working some of the problems.
• Wednesday, 1/25:
  • Class: Proof techniques: direct, contraposition, contradiction, proof by cases. Examples from "Even/odd proofs" worksheet.
  • Read/do: Try to work through the remaining problems on the handout; in particular, try the last problem (irrationality of the squareroot of 2).
• Monday, 1/23:
  • Class: More proof practice: Proofs of set-theoretic relations. "Even/odd" proofs.
  • Handout: Proof techniques and "Even/odd" proofs.
  • Homework: HW 1, due Friday, 1/27.
  • Read/do: Work through some the other problems on the handout. Particularly instructive is the second problem on even/odd squares. First try to use a direct approach and see what goes wrong; then try a proof by contraposition.
• Friday, 1/20:
  • Class: Proof practice: Proofs of set-theoretic relations.
  • Handout: How NOT to do proofs. An illustration of common errors in proofs: No explanations/justifications, no connecting words, and, most importantly, a proof going in the wrong direction (starting out a proof with the result to be proved).
  • Read/do: If you have done so, be sure to study/review the set-theoretic notations and concepts on the handout and on pp. 6 - 9 in the text, and do the problems on the handout.
• Wednesday, 1/18:
  • Class: Course overview. Handed out Course Information Sheet. Set-theoretic concepts and notation.
  • Handout: Review of set-theoretic notation and terminology.
    Solutions.
  • Read: For the next class, study/review the set-theoretic notations and concepts on the handout and on pp. 6 - 9 in the text, and do the problems on the handout. This material is quite easy, and you'll probably know much of it already from other classes, so we will not spend any further classtime on it. (On Friday, we'll use these concepts to practice some proof-writing.)