- Classes start Mon Aug 27th; Mon, Wed, Fri 12:00--12:50pm.
- Location: Math 115.
- Office Hours: Mon, Wed, Fri; 10:00--11:00.
- Homework: Set periodically and posted
to the course website.
- Exams: Announcements regarding
upcoming midterm exams will be posted here closer to the date of
- Textbook: Mathematical Proofs. A transition to advanced
mathematics. Fourth edition. By Chartrand, Polimeni and
- 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
- 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.
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