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Math 2000.002: Fall 2021

Meets: MW 2:00-3:20 in Wooten 214.

UNT encourages everyone to wear a face covering when indoors, regardless of vaccination status, to protect yourself and others from COVID infection, as recommended by current CDC guidelines. Face covering guidelines could change based on community health conditions.

Synchronous (live) sessions in this course will be recorded for students enrolled in this class section to refer to throughout the semester. Information about joining the class through Zoom will be posted on Canvas. Class recordings are the intellectual property of the university or instructor and are reserved for use only by students in this class and only for educational purposes. Students may not post or otherwise share the recordings outside the class, or outside the Canvas Learning Management System, in any form. Failing to follow this restriction is a violation of the UNT Code of Student Conduct and could lead to disciplinary action.

Remote instruction may be necessary if community health conditions change or you need to self-isolate or quarantine due to COVID-19. Students will need access to a webcam and microphone to participate in fully remote portions of the class. Information on how to be successful in a remote learning environment can be found at https://online.unt.edu/learn.

Instructor: Professor John Quintanilla

 

E-mail: John.Quintanilla@unt.edu.

 

Syllabus: http://www.math.unt.edu/~johnq/Courses/2021fall/2000/ and on Canvas.

Office: Hickory Hall, Room 256-E

Office Phone: None. Instead, please reach me by e-mail to set up an appointment to chat by Zoom or Microsoft Teams.

Office Hours: Mondays 8:30-12, or by appointment. I encourage you to make an appointment if you’re unable to see me during office hours, as I may not be able to accommodate drop-in visits. You are welcome to visit me during office hours either in person or by Zoom. The Zoom link for standing office hours will be posted in Canvas.

Required Text: Discrete Mathematics: An Introduction to Mathematical Reasoning, Brief Edition, by Susanna S. Epp. The textbook is available in both electronic and hardcopy form from the UNT Bookstore.

Strongly Recommended: The lecture notes for the semester will be available on Canvas. You are welcome to print these out at home. If you have sufficient print credits, you also can print these on campus. For more information about procedures and guidelines regarding the use of printers on campus, please see http://computerlabs.unt.edu/.

Technology: Any standard scientific calculator is acceptable for this class.

Course Description: Introduction to proof-writing, logic, sets, relations and functions, induction and recursion, combinatorics and counting techniques.

Prerequisite: Math 1650 and Math 1710 (may be taken concurrently).

Emergency Notification and Procedures. UNT uses a system called Eagle Alert to quickly notify students with critical information in the event of an emergency (i.e., severe weather, campus closing, and health and public safety emergencies like chemical spills, fires, or violence). In the event of a university closure, please refer to Canvas for contingency plans for covering course materials.

During an incident requiring individuals to take shelter, please proceed to the interior restrooms and hallways of the first floor or one of the following rooms: 122, 117, 113, 114. Avoid standing near windows, exterior walls, and doors made of glass. If you need to evacuate the building—for a fire, bomb threat, gas leak, or other event—all building occupants should immediately evacuate the building and proceed to Parking Lot 37 east of Wooten Hall. https://emergency.unt.edu/sites/default/files/wooten_hall_building.pdf


 

Course Topics

The following chapters and sections of the textbook will be covered according to the projected schedule below. Dates may change as events warrant.

  • Chapter 1: Speaking Mathematically
    • 1.2 The Language of Sets
  • Chapter 2: The Logic of Compound Statements
    • 2.1 Logical Form and Logical Equivalence
    • 2.2 Conditional Statements
  • Chapter 3: The Logic of Quantified Statements
    • 3.1 Predicates and Quantified Statements I
    • 3.2 Predicates and Quantified Statements II
    • 3.3 Statements with Multiple Quantifiers
  • Chapter 4: Elementary Number Theory and Methods of Proof
    • 4.1 Direct Proof and Counterexample I: Introduction
    • 4.2 Direct Proof and Counterexample II: Rational Numbers
    • 4.3 Direct Proof and Counterexample III: Divisibility
    • 4.4 Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder     .      Theorem
    • 4.5 Indirect Argument: Contradiction and Contraposition
    • 4.6 Indirect Argument: Two Classical Theorems
  • Chapter 5: Sequences, Mathematical Induction, and Recursion
    • 5.1 Sequences
    • 5.2 Mathematical Induction I
    • 5.3 Mathematical Induction II
    • 5.4 Strong Mathematical Induction and the Well-Ordering Principle for the Integers
    • 5.5 Defining Sequences Recursively
    • 5.6 Solving Recurrence Relations by Iteration
  • Chapter 6: Set Theory
    • 6.1 Set Theory: Definitions and the Element Method of Proof
    • 6.2 Properties of Sets
  • Chapter 7: Functions
    • 7.1 Functions Defined on General Sets
    • 7.2 One-to-One and Onto, Inverse Functions
    • 7.3 Composition of Functions
  • Chapter 9: Counting and Probability
    • 9.2 Possibility Trees and the Multiplication Rule
    • 9.3 Counting Elements of Disjoint Sets: The Addition Rule
    • 9.4 The Pigeonhole Principle
    • 9.5 Counting Subsets of a Set: Combinations
    • 9.6 Pascal’s Formula and the Binomial Theorem

 

August 23

Lecture #1

5.1 and 5.5

Sequences

August 25

Lecture #2

5.1

Series and Products

August 30

Lecture #3

5.2

Mathematical induction

September 1

Lecture #4

5.3

Mathematical induction

September 6

LABOR DAY

September 8

Lecture #5

5.4

Mathematical induction

September 13

Lecture #6

1.2

Sets

September 15

Lecture #9

2.1

Propositional logic

September 20

Lecture #10

2.2

Propositional logic

September 22

Exam #1

Lectures 1-6

Review #1

September 27

Lecture #11

2.2

Propositional logic

September 29

Lecture #12

3.1, 3.2, 3.3

Predicate logic

October 4

Lecture #13

3.1, 3.2, 3.3

Predicate logic

October 6

Lecture #14

4.1, 4.2

Writing direct proofs

October 11

Lecture #15

4.3, 4.4

Constructive proofs, counterexamples, cases

October 13

Lecture #15½

4.1-4.4

More on writing proofs

October 18

Lecture #16

4.5, 4.6

Contradiction and contraposition

October 20

Exam #2

Lectures 9-15½

Review #2

October 25

Lecture #17

4.1-4.6

More on writing proofs

October 27

Lecture #18

6.1

Set operations

November 1

Lecture #19

6.2

Proofs about sets (recording)

November 3

Lecture #19

6.2

Proofs about sets

November 8

Lecture #20

7.1

Functions

November 10

Lecture #21

7.2, 7.3

One-to-One and Onto

November 15

Lecture #22

9.2, 9.3

Combinatorics

November 17

Lecture #23

9.3, 9.4

Inclusion/Exclusion; Pigeonhole Principle

November 22

Exam #3

Lectures 16-21

Review #3

November 24

Lecture #24, 25

9.5

Combinations

November 29

Lecture #26

9.6

Binomial Coefficients and the Binomial Theorem

December 1

Lecture #26

9.6

Binomial Coefficients and the Binomial Theorem

December 6,

1:30-3:30

FINAL EXAM

 

Review #4

 


Student Responsibilities

·         Student behavior that interferes with an instructor's ability to conduct a class or other students' opportunity to learn is unacceptable and disruptive and will not be tolerated in any instructional forum at UNT. Students engaging in unacceptable behavior will be directed to leave the classroom and the instructor may refer the student to the Center for Student Rights and Responsibilities to consider whether the student's conduct violated the Code of Student Conduct. The university's expectations for student conduct apply to all instructional forums, including university and electronic classroom, labs, discussion groups, field trips, etc.

·         You should read over this syllabus carefully, as I will hold you responsible for the information herein.

·         Students will be expected to read the chapters carefully, including the examples in the book.

·         Students will be responsible for obtaining any and all handouts. If you are not in class when handouts are given, it is your responsibility to obtain copies.

·         You should begin working now. Frequent practice is crucial to the successful completion of a mathematics course. Cramming at the last minute will certainly lead to failure.

·         WARNING: If you are in academic trouble, or are in danger of losing your financial support, or if your parent or guardian is expecting a certain grade at the end of the semester... start working today. I will refuse to listen to any pleas at the end of the semester. You will receive precisely the grade that you earn.


Grading Policies

The following schedule is tentative and is subject to capricious changes in case of extracurricular events deemed sufficiently important to the upper administration.

Final Exam

17%

Exam 1

16%

Exam 2

16%

Exam 3

16%

Fibonacci Assignment

3%

Twin Primes Project

6%

Mastery Assignments

10%

Homework

16%

A

90% and above

B

80% and below 90%

C

70% and below 80%

D

60% and below 70%

F

below 60%

Cooperation is encouraged in doing the homework assignments. However, cheating will not be tolerated on the exams. If you are caught cheating, you will be subject to any penalty the instructor deems appropriate, up to and including an automatic F for the course. Refer to the following university site for the official policy with regards to academic dishonesty: http://vpaa.unt.edu/academic-integrity.htm.

The grade of "I" is designed for students who are unable to complete work in a course but who are currently passing the course. The guidelines are clearly spelled out in the Student Handbook. Before you ask, you should read these requirements.


Attendance

Attendance is not required for this class. However, you will be responsible for everything that I cover in class, even if you are absent. It is my experience that students who skip class, including students who watch recordings asynchronously, frequently make poorer grades than students who attend class regularly.

Students are expected to attend class meetings regularly and to abide by the attendance policy established for the course. It is important that you communicate with the professor prior to being absent, so you and the professor can discuss and mitigate the impact of the absence on your attainment of course learning goals. Please inform the professor if you are unable to attend class meetings because you are ill, in mindfulness of the health and safety of everyone in our community.

If you are experiencing any symptoms of COVID-19 please seek medical attention from the Student Health and Wellness Center (940-565-2333 or askSHWC@unt.edu) or your health care provider PRIOR to coming to campus. UNT also requires you to contact the UNT COVID Team at COVID@unt.edu for guidance on actions to take due to symptoms, pending or positive test results, or potential exposure.


Exam Policies

·         I expect to give exams on the days shown above. However, these are tentative dates. I will announce the exact date of each exam in class.

·         You will be expected to bring to class a calculator that can perform the calculations described in class.

·         After exams are returned in class, you have 48 hours to appeal your grade. I will not listen to any appeals after this 48-hour period.

·         I will not drop the lowest exam score; all will count toward the final grade.

·         Students missing an exam for unauthorized reasons will receive 0 (zero) points on the exam. Students will be required to provide official written verification of any authorized absences.

·         The Final Examination will be comprehensive in the sense that problems may come from any of the sections that will be covered during the semester.

·         The grade of A signifies consistent excellence over the course of the semester. In particular, an A on the final is not equivalent to an A for the course.

·         I reserve the right to test and quiz you on problems which are generalizations of material covered in the class and/or in the text. In short, the problems may not look exactly like the ones in the book.

·         Everything that I say in class is fair game for exam material. You will be responsible for everything unless I advise you to the contrary.


Homework and Project Policies

·         Homework will be assigned and collected via Canvas and will be due Wednesdays at 11:59 pm, except for the final assignment due the week after Thanksgiving.

·         Homework should be uploaded as a single PDF file. Options for converting your hand-written work into PDF format:

·         I expect the assignments that you turn in to be written up carefully and neatly, with the answers clearly marked. You must show all of your work. Messy homework will not be accepted.

·         Entire homework assignments will not be graded. Instead, only five representative problems will be graded per assignment. As a consequence, it will be possible to not do the entire assignment and still receive a perfect score on that particular assignment. Deliberately leaving homework uncompleted is highly unrecommended, however, as the law of averages will surely catch up with you as the semester progresses.

·         When computing grades, I will drop the two lowest homework grades before computing the homework average. Therefore, in principle, you could get a 100% homework score and also not turn in two assignments during the semester. I have this policy in case you get sick, a family emergency arises, etc., during the semester. You will still be responsible for the material in such assignments during the examinations.

·         I will not give extensions on homework assignments, nor will I accept late assignments.

·         Two class projects (on the Fibonacci numbers and on the Twin Primes Conjecture) will be assigned on Canvas.

·         Mastery assignments on different topics will be assigned throughout the semester. Unlike regular homework assignments, you can attempt these weekly, and your highest score will count toward the final grade. So, for example, if you get a perfect score on your first attempt for a certain topic, there will be no need to re-attempt that same topic.


Note to TNT Students

·         If you’re pursuing secondary teacher certification through Teach North Texas, then you may be aware that you will be required to construct a preliminary teaching portfolio in EDCI 4500 (Project-Based Instruction) and a final portfolio during your final semester of student teaching. Section 2 of this portfolio will ask you to demonstrate your knowledge of your content field. You may find that some of the assignments may naturally become artifacts toward part of this task, and so I encourage you to keep your work after the semester is over to make the eventual construction of your portfolio easier. You may even want to write (and save for later) a brief reflection on the artifact you select, rather than try to remember why the artifact you chose was important once you reach EDCI 4500.

·         The specific indicators in the portfolio related to knowledge of mathematical content are as follows:

o    Reflect on one or more artifacts in which you state a mathematical theorem or conjecture and apply both formal and informal mathematical reasoning to the same conjecture.

o    Reflect on one or more artifacts that show your ability to describe a mathematical concept that can be represented in multiple ways and articulate the connections between its representations in clear, expository prose. Where relevant, identify appropriate technology for exploring the concept and explain limits the technology may place on the knowledge acquired.

o    Reflect on one or more artifacts that show your ability to generate a model of a natural phenomenon or describe an already existing model and evaluate how well the model represents the situation, including consideration of the risks, costs, and benefits of the alternatives.

o    Reflect on one or more artifacts that show your ability to identify a topic in your subject area and describe its connection with prerequisite topics, future topics, and other subjects.

o    Reflect on one of more artifacts that show how you bring out the historical and cultural importance of your subject material, its contribution to large ideas, and its significance in today’s society. Include a specific lesson plan that incorporates the general history and cultural context of modern science or of mathematics as these fields have evolved.

·         Just to be clear: the above are suggestions for TNT students. This is NOT a course requirement for Math 2000.


Final Note

The University of North Texas makes reasonable academic accommodation for students with disabilities. Students seeking accommodation must first register with the Office of Disability Accommodation (ODA) to verify their eligibility. If a disability is verified, the ODA will provide you with an accommodation letter to be delivered to faculty to begin a private discussion regarding your specific needs in a course. You may request accommodations at any time, however, ODA notices of accommodation should be provided as early as possible in the semester to avoid any delay in implementation. Note that students must obtain a new letter of accommodation for every semester and must meet with each faculty member prior to implementation in each class. For additional information see the Office of Disability Accommodation website at http://www.unt.edu/oda. You may also contact them by phone at 940.565.4323.