Course: Math 310, Math 310W, Foundation for Higher Mathematics
Class hours: MWF 1-2 pm for both Math 310 and Math 310W, and an extra M 11-12pm for students taking Math 310W
Classroom: Cupples I, Room 115, for both Math 310 and math 310W, and Cupples I, Room 216, for Math 310W
Instructor: Quo-Shin Chi
Office: Room 210, Cupples I
Office Hours: TBA
Textbook: Class Notes

       We shall rigorously go through the construction of real numbers. By "rigorously" we mean we adopt the axiomatic approach to follow precise logical arguments to deduce important properties (theorems) from the chosen basic postulates (axioms), while along the way we introduce definitions to facilitate our train of thoughts. More precisely, we assume intuitive properties of sets, and start with the Peano axioms for natural numbers to build the four operations +, -, *, / for them. We then extend from natural numbers to integers, rational numbers and finally real numbers and their corresponding operations +, -, *, / . The construction of real numbers is the most subtle of all, to which there are several approaches. To let the students be as comfortable and skillful as possible with the notion of limits that is paramount in more advanced courses, we shall adopt the method in which a real number is identified with an equivalence class of convergent Cauchy sequences of rational numbers. If we have time, we shall cover some material from elementary number theory of integers.

       For students taking 310W, the first few hours of our Monday session will be devoted to the basics of writing with LaTex. All your homework sets, except for the first one or two, should be typeset in LaTex. Moreover, we will have three essay papers, each about six pages long, such as a report on Fermat's last theorem, etc., to write during the semester. We will discuss in class the writings of your homework solutions; you will then be asked to rewrite the part deemed incorrect or unclear and submit it one last time. Based on this revision you will be assigned a fraction of 1 point (you automatically get 1 point if your solution was all correct to begin with). These points accumulated will be contributed to your overall score of the writing session, on top of the scores given to the essays.  
   
      For students taking Math 310, there will be homework assignments (30%), one take-home midterm (30%) and one take-home final (40%). For those who take 310W, the above scale will constitute only 85% of  your overall score, whereas the writings will constitute the remaining 15%.

Class Notes 1

Class Notes 2

Homework 1

Class Notes 3

310W LaTex Script

Homework 2

Homework 1 Solution

Homework 3

Homework 4

Class Notes 4

Homework 2 Solution

Class Notes 5

Homework 3 Solution

Homework 4 Solution

Midterm

Homework 5 Solution

Class Notes 6

Midterm Solution

Class Notes 7

Final