COURSE SYLLABUS

Course Number: MATH3100
Course Title: INTRODUCTION TO ADVANCED MATHEMATICS
Credit Hours: 3
Prerequisites: MATH2630
Corequisite: 

Objectives: 
The systematic approach to the teaching of fundamental abilities necessary for the pursuance of mathematical studies. In particular: the ability to think logically, and the ability to write and present a correct mathematical proof, are two of the fundamental skills of advanced mathematics which will be covered in the course. 

Schedule and Outline of Course Content: 
1. Basic Logic and Set Theory (about 3 weeks)
        The Language of Mathematics: Truth Tables, Quantifiers, Elementary Proof Techniques, Basic Set Theory (How to show two sets are equal), Relations and Functions, Countable and Uncountable Sets: Countability of the rational numbers, Existence of uncountable sets
2. Mathematical Induction (about 11/2 weeks)
        Proof by Induction, Recursion
3. Basic Number Theory (about 31/2 weeks)
        Counting and Permutations, The Binomial Theorem
         Divisibility: Prime Factorization, Existence of infinitely many primes, The Division Algorithm, The Euclidean Algorithm
         Modular Arithmetic: Equivalence relations, The integers mod n
4. Basic Analysis (about 6 weeks)
        The Completeness Axiom, Uncountability of the real numbers
        Sequences and Series: Cauchy Sequences,  Bolzano-Weierstrass Theorem
        Limits and Continuity: The epsilon-delta definition of Limits and Continuity, Intermediate Value Theorem, Continuity and Closed Intervals
        Series of Functions, Pointwise and Uniform Convergence
5.  Writing and presenting mathematical Proofs  (Not done separately, but integrated into the above material throughout the semester).

Possible textbooks:
Mathematical Thinking; Problem Solving & Proof, John P. D'Angelo, Douglas B. West, Prentice Hall,



Sample Grading and Evaluation Procedures:

Students will be expected to be prepared for class by doing assigned homework exercises.  An important part of the course is learning how to prove theorems.  Students will be expected to provide their own proofs of theorems and solutions to mathematical problems posed in class.  The presentation of proofs and solutions is an important part of the grade. Similarly class participation will also be a component of the grade.   Homework will occasionally be collected. Quizzes may be unannounced. 

Grade Calculation
Participation grade 
(includes: classwork, attendance, homework, quizzes):					10%
Blackboard presentation: 									20%
Hour Tests (three hour tests):								40%
Final Exam:										30%

Tentative Test Schedule
Hour tests are given at the end of appropriate units and will be announced a week ahead of time.  Quizzes may or may not be announced; at least four quizzes will be given in the course of the semester.  Friday is typically a good day for quizzes. 

Sample Statement Re: Accommodations

	Students who need accommodations are asked to arrange a meeting during office hours the first week of classes, or as soon as possible if accommodations are needed immediately.  If you have a conflict with my office hours, an alternate time can, be arranged.  To set up this meeting, please contact me by E-mail.  Bring a Copy of your Accommodation Memo and an Instructor Verification Form to the meeting.  If you do not have an Accommodation Memo but need accommodations, make an appointment with The Program for Students with Disabilities, 1244 Haley Center, 844-2096 (V/TT).  (Note: Instructor office room, office hours and email address will be made available on the course syllabus and on the first day of class.)