Course Goals: This course introduces mathematics majors to mathematical reasoning, which is the basis for all your further theoretical work in mathematics. You will be introduced to proof through both formal logic (propositional calculus, truth tables, quantification) and informal arguments, including direct proofs, proofs by contradiction, and proofs using mathematical induction. You will do proofs in set theory and functions, factorials and recurrence, counting techniques, introductory number theory, and introductory graph theory. You will gain experience in writing correct mathematical definitions, determining whether a mathematical statement is true or false, and how to justify these conclusions.
 

Course Student Learning Objectives: By the end of the course, you will be able to:

• Develop simple direct, indirect, and inductive proofs
• Give accurate proofs of a few important classical theorems
• Prove statements from set theory
• Demonstrate understanding of elementary topics from graph theory and number theory via computations, explanations, and proofs
• Solve elementary combinatorial problems
• Demonstrate an understanding of the definition of function and a range of special kinds of functions, such as permutations and recursively defined functions
• State mathematical definitions correctly
• Translate mathematical statements between English and mathematical symbolism

Course Requirements:  In-class group work, homework, definition quizes, proof portfolio, 3 in-class examinations, cumulative final examination.

Methods of Evaluation and Grading Policy:  Each in-class examination will constitute 15% of the grade, the final examination will constitute 25% of the grade, 5% of the grade will come from classwork, 5% from definition quizes, 5% from your proof portfolio, and the remaining 15% of the grade will come from homework.

On a scale of 0 to 100, grades of:

A and A- will be assigned to scores of 90 and above

B+, B and B- will be assigned to scores between 80 and 90

C+, C and C- will be assigned to scores between 65 and 80

D+, D and D- will be assigned to scores between 50 and 65

F will be assigned to scores below 50.

Statement on Academic Honesty:  Except for two sets of special supplementary problems, you are welcome to consult others, whether students in the class or tutors in the Mathematics Learning Center.  However, whenever you have had assistance with a problem, you are to state that at the beginning of the solution to the problem.  Unless it becomes excessive, there will be no reduction in credit for getting such assistance.

Examination Rules:  No student is permitted to have at his or her desk any books or papers that are not given out by the instructor.  Possession of such material will be regarded as evidence of intent to use the information dishonestly.  No communication between students during the examination is permitted.  If there are questions, or if there is a need for additional material, the instructor should be asked.  Details of calculations should be written on the pages of the exam.  In accordance with the academic honesty policy of Monmouth University each exam will contain the following pledge:

“I, ____________________________, certify that I have read the rules for examinations, and that I have abided by them. By signing, I affirm that I have neither given nor received aid during this examination, and I understand that violation of this affirmation may result in suspension or expulsion from Monmouth University.”

Statement on Special Accommodations:  Students with disabilities who need special accommodations for this class are encouraged to meet with me or the appropriate disability service provider on campus as soon as possible.  In order to receive accommodations, students must be registered with the appropriate disability service provider on campus as set forth in the student handbook and must follow the University procedure for self-disclosure, which is stated in the University Guide to Services and Accommodations for Students with Disabilities.  Students will not be afforded any special accommodations for academic work completed prior to the disclosure of the disability, nor will they be afforded any special accommodations prior to the completion of the documentation process with the appropriate disability office.

Outline of Course Content and Schedule:

When there is an asterisk (*) after a problem number, it means that further directions will be given in class.  Homework is due on the following class day.  So, for example, on 1/19, we’ll discuss the reading from section 1.1 of the Notes (you are expected to read this before class), and the homework listed on that day is due in class on 1/23.  Unless otherwise stated, the homework is from the same section as the reading.

You are expected to do the reading for the day before coming to class.