Math 3310

Textbook: Mathematical Proofs. A transition to advanced mathematics. Fourth edition. By Chartrand, Polimeni and Zhang.

Outline: The purpose of the course is to introduce mathematics as a process of logical reasoning rather than merely calculation. We will study logic, the language of mathematics. We will learn what a proof in mathematics is, how to understand a written proof and how to construct our own. The topics from the book that I intend to cover are:

1.1 Describing a Set
1.2 Subsets
1.3 Set Operations
1.4 Indexed Collections of Sets
1.5 Partitions of Sets
1.6 Cartesian Products of Sets
2.1 Statements
2.2 The Negation of a Statement
2.3 The Disjunction and Conjunction of Statements
2.4 The Implication
2.5 More on Implications
2.6 The Biconditional
2.7 Tautologies and Contradictions
2.8 Logical Equivalence
2.9 Some Fundamental Properties of Logical Equivalence
2.10 Quantified Statements
2.11 Characterizations of Statements
3.1 Trivial and Vacuous Proofs
3.2 Direct Proofs
3.3 Proof by Contrapositive
3.4 Proof by Cases
4.1 Proofs Involving Divisibility of Integers
4.2 Proofs Involving Congruence of Integers
4.3 Proofs Involving Real Numbers
4.4 Proofs Involving Sets
4.5 Fundamental Properties of Set Operations
4.6 Proofs Involving Cartesian Products of Sets
5.1 Counterexamples
5.2 Proof by Contradiction
5.4 Existence Proofs
5.5 Disproving Existence Statements
6.1 The Principle of Mathematical Induction
6.2 A More General Principle of Mathematical Induction
6.3 Proof by Minimum Counterexample
9.1 Relations
9.2 Properties of Relations
9.3 Equivalence Relations
9.4 Properties of Equivalence Classes
9.5 Congruence Modulo n
9.6 The Integers Modulo n
10.1 The Definition of a Function
10.2 One-to-one and Onto Functions
10.3 Bijective Functions
10.4 Composition of Functions
10.5 Inverse Functions
Note: This syllabus may be subject to modest alterations in content as the semester progresses. Some topics from chapters 10 and 11 will be covered if time permits.

Homework assignments will contribute to 10% of your grade. It is important that you hand them in on time.
There will be two midterm exams. Each midterm exam will be worth 25% of your grade.
There will be a final exam, which will be worth 40%.

Absences: You must inform me as soon as possible if you are or intend to be absent for an exam. Makeup exams will only be offered for legitimate absences such as university sanctioned activities and in the case of illness, which must be supported by a note from your physician.
Academic Integrity: It is the aim of the faculty of Texas Tech University to foster a spirit of complete honesty and high standard of integrity. The attempt of students to present as their own any work not honestly performed is regarded by the faculty and administration as a most serious offense and renders the offenders liable to serious consequences, possibly suspension. “Scholastic dishonesty” includes, but it not limited to, cheating, plagiarism, collusion, falsifying academic records, misrepresenting facts, and any act designed to give unfair academic advantage to the student (such as, but not limited to, submission of essentially the same written assignment for two courses without the prior permission of the instructor) or the attempt to commit such an act. In particular:

The submission of any work for credit (be it homework or exam) that has been copied from another source (including another person) will be regarded as an act of academic misconduct.
You are permitted to seek help from other students, faculty members or private or Texas Tech tutors for homework problems only. However, any work submitted must be your own and reflect your own understanding of the material and not be merely copied or recited from another source or person (see above).
Seeking or receiving aid from another source during an exam (including another person, who is not the instructor or proctor) will be regarded as an act of academic misconduct. You may be permitted to bring some notes into the examination -- I will provide instructions in advance.
The use of phones and smartwatches during any examination is not permitted. Calculators may be permitted -- I will provide instructions in advance.
This list is not exhaustive. You may consult the Student Handbook Part I Section B for further guidance and examples. If you are unsure whether any of your planned actions might constitute academic misconduct you should consult with me first in writing (through email).

ADA Accommodation: Any student who, because of a disability, may require special arrangements in order to meet the course requirements should contact me as soon as possible to make any necessary arrangements. Students should present appropriate verification from Student Disability Services. Please note: instructors are not allowed to provide accommodations to a student until appropriate verification from Student Disability Services has been provided. For additional information, you may contact the Student Disability Services office in 335 West Hall.
Religious Holidays: A student shall be excused from attending classes or other required activities, including examinations, for the observance of a religious holy day, including travel for that purpose. A student who intends to observe a religious holy day should make that intention known to me in writing prior to the absence. A student who is absent from classes for the observance of a religious holy day shall be allowed to take an examination or complete an assignment scheduled for that day within a reasonable time after the absence.