Mainpage Syllabus Recitations Calendar Homework Links

Syllabus for 15-151 and 21-128

Course Outline: The ability to reason logically and clearly from a set of accepted principles is fundamental not only in Mathematics, but in Life in general. In this class we will learn how to provide complete explanations of why certain things are true. We will also determine how to detect false statements and provide conclusive evidence of their falsity.

We will begin with concrete objects like numbers, sets and functions and learn to prove things about them using elementary logic. After studying a proof technique known as induction, we will explore functions and use them to classify the size of infinite sets (yes, there are different sized infinite sets).

Next we will find out how to count the number of objects that can be obtained as the result of a certain process. For example, we can count the number of distinct poker hands which have three aces and two kings or the number of different three-topping pizzas that can be made if ten toppings are available. We then tackle elementary problems concerning integers, such as factorization, divisibility and their possible applications to cryptography.

Lastly, we will study some classic topics from Discrete Math. Elementary probability will be explored in order to ascertain, for example, just how likely are we to be dealt a poker hand containing three aces and two kings. We will see that probability is related to counting and will move on to study useful topics in counting known as the pigeonhole principle and inclusion/exclusion.



Classes and Recitation Sessions: 21-128 meets via Zoom MWF from 12 to 12:50. 15-151 meets via Zoom MWF from 2:40-3:30. Here is a Zoom link for the class sessions: Classes

Our wonderful Teaching Assistants will also hold two weekly recitation sessions. I strongly encourage you to attend the recitation sessions as they are an integral part of the course and may cover examinable material not covered in lecture.



TA Zoom (not Office) Hours: Click here for the calendar of Teaching Assistant Zoom (not Office) Hours.

We will be holding office hours online this semester. Students will go to the OHQ website ( OHQ) and upon logging in, find the 21-128/15-151 queue. When adding themselves to the queue, students must add a link in the description box to their personal zoom meeting so that TAs can provide them (and any collaborators) with help. They can also include a brief description as to their question(s). At the top of the hour, the TA will enter the zoom room linked in the calendar to discuss general questions. This room will be open for the entire OH period for students to enter and leave freely.

Remote Classes and Recitations: Students have the option of attending lectures and recitations remotely. These will be scheduled and conducted through Zoom, and we will be solely using the remote instruction method for all lectures and recitations after Thanksgiving. Please make sure to have a computer with a good internet connection and a good web camera for remote instruction and exams. In particular, we will proctor remote exams through Zoom and it is a requirement that students taking remote exams use a webcam to clearly display their testing environment throughout the exam.

In the event of a poor internet connection (for either students or instructors), lectures and recitations will be recorded and made available to watch at a later time.



Instructor's Office: Gates 4005        Phone:268-1204       Email:jmackey@andrew.cmu.edu


Course Website:  www.math.cmu.edu/~jmackey/151_128/welcome.html


Instructor Zoom (not Office) Hours: Tuesday from 1:00-2:00, Wednesday from 10:15-11:15, and by appointment: Mackey Zoom Hours

Help: In addition to class, recitation sessions, and zoom (not office) hours, the University operates Peer Tutoring Centers. Individualized tutoring and other help options are also available through Academic Development.



Book: An infinite descent into pure mathematics -> https://infinitedescent.xyz/
An infinite descent into pure mathematics , default, by Clive Newstead.
An infinite descent into pure mathematics , tablet, by Clive Newstead.
An infinite descent into pure mathematics , smartphone, by Clive Newstead.
An infinite descent into pure mathematics , print, by Clive Newstead.



Supplemental (optional) Book: Everything You Always Wanted To Know About Mathematics , by Brendan Sullivan


Supplemental (optional) Book: Mathematical Thinking: Problem-Solving and Proofs (2nd Edition), by D'Angelo and West



Homework: Homework exercises are an essential part of the course. It is difficult to understand the material and do well on the exams without working through the homework problems in a thoughtful manner. Discussion of the homework with your peers is encouraged, but copying any part of another person's homework is not permitted. Please think about the problems posed, your strategies, and the validity of your logic and explanations.

Homework is to be submitted through Gradescope by the required due date and time. Homework that is submitted after the due date and time, but before the solutions are posted will receive half credit (with an asterisk to get full credit if the course grade is borderline). Each homework solution set that is typeset using LaTex will earn a one point bonus, beginning with the second homework assignment. If you choose to handwrite and then scan homeworks, then here is a helpful resource for scanning documents on campus: Scanning documents

Homework and Exam regrade requests must be submitted within one week of the return date.



Midterms: There will be three midterms and a cumulative final exam. The dates of the midterm exams are as follows:


Midterm 1: Monday, September 28

Midterm 2: Wednesday, October 28

Midterm 3: Monday, November 23


Grading: Your course grade will be determined as follows:

Each of the two high midterm scores: 20%
The low midterm score: 10%
Homework: 20%
Final Exam: 30%

The highest possible grade cutoffs will be 90% for an A, 80% for a B, 70% for a C, and 60% for a D. These cutoffs may be lowered slightly, but will not be increased.



Calculators: Calculators will not be useful in this course. Calculators and other electronic devices will not be allowed during the exams.




Wellness: Take care of yourself. Do your best to maintain a healthy lifestyle this semester by eating well, exercising, avoiding drugs and alcohol, getting enough sleep and taking some time to relax. This will help you achieve your goals and cope with stress.

All of us benefit from support during times of struggle. You are not alone. There are many helpful resources available on campus and an important part of the college experience is learning how to ask for help. Asking for support sooner rather than later is often helpful.

If you or anyone you know experiences any academic stress, difficult life events, or feelings like anxiety or depression, we strongly encourage you to seek support. Counseling and Psychological Services (CaPS) is here to help: call 412-268-2922 and visit their website at http://www.cmu.edu/counseling/. Consider reaching out to a friend, faculty or family member you trust for help getting connected to the support that can help.

If you or someone you know is feeling suicidal or in danger of self-harm, call someone immediately, day or night:

CaPS: 412-268-2922

Re:solve Crisis Network: 888-796-8226

If the situation is life threatening, call the police:

On campus: CMU Police: 412-268-2323

Off campus: 911

If you have questions about this or your coursework, please let me know.




Research on student learning: Marsha Lovett, Laura Pottmeyer and I are conducting research on how students learn in this course. The research will involve analyzing data from this course and 15-051. You will not be asked to do anything above and beyond the normal learning activities and assignments that are part of this course. You are free not to participate in this research, and your participation will have no influence on your grade for this course or your academic career at CMU. If you choose not to participate in the research, you must still complete all required coursework, but your data will not be included in the research analyses. Participants will not receive any compensation. The data collected as part of this research will include student grades. All analyses of data from participants coursework will be conducted after the course is over and final grades are submitted. The Eberly Center may provide support on this research project regarding data analysis and interpretation. To minimize the risk of breach of confidentiality, the Eberly Center will never have access to data from this course containing your personal identifiers. All data will be analyzed in de-identified form and presented in the aggregate, without any personal identifiers. Please contact Chad Hershock (hershock@andrew.cmu.edu) of the Eberly Center if you have questions or concerns about your participation.


Week by week schedule (tentative):

Week 1 (August 31 - September 4):

  • Introduction and Chapter 0
  • 1.1
  • 1.2

Week 2 (September 8 - 11):

  • 1.2
  • 2.1

Week 3 (September 14 - 18):

  • 2.2
  • 2.2
  • 3.1

Week 4 (September 21-25):

  • 3.2
  • 4.1
  • 4.2

Review for Midterm; Friday, September 25

First Midterm; Monday, September 28

Week 5 (September 28 - October 2):

  • First Midterm
  • 4.2
  • 4.3

Week 6 (October 5 - 9):

  • Inductionfest 2020
  • 5.1
  • 5.2

Week 7 (October 12 - 15):

  • 6.1
  • 6.2
  • 6.2

Week 8 (October 19-22):

  • 6.3
  • 7.1

Review for Midterm; Monday, October 26

Second Midterm; Wednesday, October 28

Week 9 (October 26 - 30):

  • Review for Midterm
  • Second Midterm

Week 10 (November 2 - 6):

  • 7.1
  • 7.2
  • 7.2

Week 11 (November 9 - 13):

  • 7.2
  • 8.1
  • 8.1

Week 12 (November 16 - 20):

  • 9.1
  • 9.1
  • Review for Third Midterm

Review for Midterm; Friday, November 20

Third Midterm; Monday, November 23

Week 13 (November 23 - 24):

  • Third Midterm

Week 14 (November 30 - December 4):

  • 10.1
  • 10.1
  • 10.1

Week 15 (December 7 - 11):

  • 10.2
  • 10.2
  • Review for Final Exam

Final Examination, Scheduled by the Registrar

Return to Welcome Page



Please send comments to jmackey@andrew.cmu.edu