Recommended Reading: Math SciFi. "And He Built a Crooked House", by Robert Heinlein.

Class Meetings : 12PM to 12:50PM, 204BH, MWF.

Office Hours: 3PM to 4PM on MWF.

Prereqisites: Grade of C or better in MATH 181 and approval of the department.

Description: This is a first course in theoretical mathematics. It is a prerequisite to all advanced theoretical courses in the department. The primary goal of the course is to learn how to create and write mathematical proofs. We will introduce basic proof techniques, such as proofs by induction and contradiction and the course will cover symbolic logic, basic set theory and some selected topics in combinatorics, geometry, topology and number theory. As time permits, we will cover most of Parts I-III and parts of Part V of the text.

The course will proceed via projects and problems. We will begin by using the text by Eccles to work on basics of logic, sets, proof by induction and problems involving sets and arithmetic.

Because the course is structured through evolving problem sets and projects, it is essential that you WORK ON THE PROBLEMS AND ATTEND ALL THE CLASSES. There is no recourse here to staying away from class. If you miss a class, please see the instructor and get a recapitulation of what went on in that class. Credit in the course will be a function of your homework, projects and the exams.

See ASSIGNMENT1 Here is the first assignment. It is due on Friday 20, January 2012.

See Four Knights Here is a Java Applet that will help in working on the first problem in Assignment Number One.

See ASSIGNMENT2 Here is the second assignment. It is due on Monday, January 30, 2012.

See ASSIGNMENT3 Here is the third assignment. It is due on Friday, February 10, 2012.

The FIRST HOUR EXAM will be at classtime on Wednesday, February 15, 2012.

See ASSIGNMENT4 Here is the fourth assignment. It is due on Friday, February 24, 2012.

See ASSIGNMENT5 Here is the fifth assignment. It is due on Friday, March 9, 2012.

See ASSIGNMENT6 Here is the sixth assignment. Along with the book assignments, read the Rudin notes and the Infinite Sets notes. For a hint on Problem 9 see the link below. This assignment is due on Monday, April 2, 2012. Please note that therre are 12 problems with parts, and that the problem set has been expanded.

ASSIGNMENT 7 -- DUE ON APRIL 20, 2012. Here is the seventh assignment. Read Chapters 15,16,17, 19, 23 and 24. Problem 1: InfiniteHotel. This is a cartoon story about an infinite hotel that can seemingly accomodate any new influx of guests. Read the story carefully and explain how it is related to the uncountability of the set of subsets of the natural numbers. Problem 2: ConwayArmy. This is a description of a game and a theorem about the game. Read this short article, try playing the game (use coins and a sheet of paper or a checker board), and write a summary in your own words of the mathematics in the article. Problem 3: Eccles p. 197. 15.1, 15.3. 15.5, 15. 6; Eccles p. 206. 16.1; Eccles p. 215. 17.1, 17.2; Eccles p. 239. 19.3.

ASSIGNMENT 8 -- This last assignment concentrates on Chapter 23. Eccles Page 287. Problems 23.1, 23.2, 23.3, 23.4. Eccles Page 294. Problems 24.1, 24.3, 24.5. You are not required to hand in this set of problems, but the final exam will contain a problem related to these problems.

CLASS WILL MEET ON FRIDAY, APRIL 27, 2012. WE WILL HAVE A GUEST LECTURER - LENA FOLWACZNY. LENA WILL BE HAPPY TO ANSWER YOUR QUESTIONS AND SHE WILL TALK ABOUT HOW WE APPLY MODULAR ARITHMETIC TO STUDYING THE TOPOLOGY OF KNOTS IN THREE DIMENSIONAL SPACE.

FINAL REVIEW SESSION WILL BE ON MONDAY, APRIL 30, 2012 IN 612SEO FROM 1PM TO 5PM. TO REVIEW FOR THE FINAL, SEE THE SAMPLE EXAMS BELOW. RECALL FOR YOURSELF THE DIFFERENT FORMS OF PROOF THAT WE HAVE STUDIED. REVIEW ALSO THE DIFFERENT SPECIFIC PROOFS THAT WE HAVE EXAMINED IN LOGIC, GRAPHS AND COMBINATORICS, IN SET THEORY AND IN NUMBER THEORY. ONE EXAM QUESTION THAT IS VERY LIKELY IS: "STATE AND PROVE A THEOREM WHOSE PROOF YOU ENJOY."

THE FINAL EXAM WILL BE ON TUESDAY, MAY 1, 2012 IN 204BH (the classroom we have been using for the course) FROM 8:00AM TO 10:00AM.

See SAMPLE FINAL1 , SAMPLE FINAL2 , SAMPLE FINAL3 , PROBLEM SAMPLER . These are three previous final exams and a list of sample problems.

See Inclusion-Exclusion This is a paper relevant to Problem 9 in Assignment 6.

See Cantor-Schroeder-Bernstein This is a proof of the Cantor-Schroeder-Bernstein Theorem.

See SAMPLE EXAM This is a sample second exam. THE SECOND EXAM WILL BE ON MONDAY, APRIL 9, 2012.

See SAMPLE EXAM This is a sample first exam.

See Geometry. A short article about plane geometry, the pentagon and the golden ratio.

See Set Theory. This is a concise set of notes on basic set theory, taken from the book "Principles of Mathematical Analysis" by Walter Rudin.

See Infinite Sets. These are supplementary notes on infinite sets.

See Calculus. This is a set of notes on calculus using infinitesimals.

See Boolean Notation. A short article about Boolean Algebra notation.

See Peano Axioms for a list of the Peano axioms for the natural numbers and a list of problems to prove, using these axioms. We will discuss the problems in class after learning more about induction.

See Landau's Foundations for a working out of the Peano axioms from a classic book by Edmund Landau. Landau wrote his book in 1929 and you should read the introduction for the student to experience his very upright attitude toward learning mathematics.

See Conway's Sprouts. This is an excerpt from the book "Winning Ways for Your Mathematical Plays" by Conway, Berlekamp and Guy. It contains information about the game of sprouts.

See ContFrac. This is a calculator on the web that converts numbers to their continued fracations. Try it on sqrt(2), sqrt(3), e, pi and other favorite numbers.

See VanPoorten. This is an excellent article on continued fractions.

See Recreations. This is an access page to programs and mathematical recreations.