CMPE 016 - Applied Discrete Mathematics

J.J. Garcia-Luna-Aceves
(jj "a_t" soe. ucsc. edu)
Office: E2 317
or E2 315 (CCRG Lab)
Office Hours: Mondays 3:50 to 5:00 pm
You can email me to meet at different times
TA: Jane Li
(zhil "at"
TA: Elinor Velasquez
(elinor "at"
MSI Tutor:
Priera Panescu
( ppanescu "at"
Baskin Engineering Auditorium 101
T Th 4:00 pm - 5:45 pm
Discussion (01A)
Engineering 2 194
Wed 5:00 pm-6:10 pm
Discussion (01B)
Engineering 2 194
Wed 7:30-8:40 pm
Discussion (01C)
Engineering 2 194
Thu 8:30 am-9:40 am
Discussion (01D)
Engineering 2 194
Fri 9:30 am-10:40 am

MSI Session
ARCenter 221
Mon 11--12:10
MSI Session
ARCenter 221
Tue 2--3:10
MSI Session
Crown 105
Wed 3:30--4:40

News| Class Description| Grading| Student Responsibilities| Academic Integrity| Forums will be done through eCommons | Textbook| Syllabus| Homeworks | Homework Solutions | Requesting Academic Accommodations | On-Line Grades

Please report any problems to JJ.


Last lecture today! sigh! time went so fast!
Quiz 4 grades are posted and reviewed. Stats shown as ususal.
You can pick up graded quiz 4 in class or tomorrow during TA section.
Solutions to sample final are posted in teh HW page.
We will review the sample final and a few last proofs today.
Wishing you teh very best outcome in finals week!!!


Slides for today's lecture are uploaded.
Quiz 4 solutions are posted in homework page.
Solutions to some probelms for HW 7 to be posted tonight.
I am still reviewing Quiz 4. Will return them on Thu in class.


Updated slides for 5-21 lecture uploaded.
Sample final uploaded in homeworks page. We will go over it this coming Thursday.
Probability questions posted.


Slides for 5-30 lecture uploaded.
The stats for grades in the midterm are posted.
Based on the results in the midterm, we will drop the worst quiz grade for the average of all quizzes.
However, those doing great please consider Quiz 4 as practice for the final!


Sample quiz 4 posted in the homeworks page. Expect 30min, 4 to 5 questions, closed book, closed notes.
Updated slides for 5-16 lecture uploaded.
Graded midterms will be distributed starting TOMORROW (Wed.) at the discussion sections.


Solutions to midterm posted in the homeworks page.


I uploaded the doc cam notes from yesterday, AND additional notes regarding strong induction.
Good luck tomorrow!!!


Solutions to Quiz 3 and sample midterm posted in homeworks page.
Contact your TA regarding your grade in Quiz 3 if you have questions.
Updated version of lecture set for 5-09 is uploaded.


Slides for 5-16 and 5-21 lectures are uploaded.
IMPORTANT: Date for Midterm is changed to THU May 23!!
Sample midterm posted in homeworks page.


Slides for 5-14 lecture uploaded.
Homework 6 posted.


Document camera notes from 5-7 lecture uploaded.
Remember to ask all your Qs on induction this week!!
Slides for 5-09 lecture uploaded.


Solutions to Sample Quiz 3 uploaded.
Can you see that strong induction is *really* simple? :-)


Class notes for 5-07 uploaded.


Solutions to Quiz 2 posted in the homeworks page.

Sample Quiz 3 posted in homeworks page!


More typo fixes for 4-30 notes uploaded.


Updated notes for 4-30 uploaded, notes for 5-2 uploaded.


Homework 5 is posted.


Slides for 4-30 lecture are uploaded.


4-25 class notes from doc camera uploaded.

Sample Quiz 2 available in the Homeworks Page.
Make sure you ask your Qs on proof methods BEFORE Wed!!!!


Slides for Lecture 4-25 uploaded.
We still have to finish slides from 4-18 and 4-23, though.
Doc camera notes for 4-23 uploaded.


Solutions to HW 3 even-number problems posted.


Slides for 4-23 lecture are uploaded.
Document camera scans for 4-18 lecture are uploaded.
eCommons is up and you will be able to check your grades on-line.
Homework 4 is assigned.


Slides for 4-18 lecture are uploaded.


Solutions to HW 2 are uploaded.
HW 3 is assigned.
Sample for Quiz 1 in the homework page.


Slides for Sections 1.4 to 1.6 are uploaded.

Solutions to HW 1 are uploaded.
HW 2 is assigned.
Material for Quiz 1:
You must know how to solve problems in HWs 1 and 2, and you must understand Sections 1.1 to 1.3, and Section 2.1.


Scans of textbook pages with HW 1 problems are uploaded.
You can find them in the homeworks page.


Slides of first lecture uploaded!
Slides of tomorrow's lecture have been uploaded. There are two parts, so please get both.
Try to go over the material befor class if you can.
Note: Slides for 4-9 and 4-11 lectures are uploaded too!


Welcome to the Spring quarter!

Class Description

This course provides introduction to applications of discrete mathematical systems. The core topics covered in this course are:

  • Logic: propositions, proofs using propositional equivalences.
  • Sets and set operations.
  • Predicates, quantifiers.
  • Rules of inferene and mathematical proof methods.
  • Functions and relations, sequences and summations.
  • Mathematical induction.
  • Recursive definitions.
  • Counting arguments, pigeonhole principle, permutations and combinations.
  • Inclusion-exclusion principle.
  • applications of the binomial coefficient and factorials.
  • generalized permutations and combinations.
  • Introduction to solving recurrence relations, n-ary relations.
  • Discrete probability.
  • Applications: Algorithms
  • Applications: Boolean algebra and logic circuits
  • Applications: Modular arithmetic
Optional topics include trees and incudction on trees, generating functions.

Examples are drawn from computer science and computer engineering.

Prerequisites: Eligibility to enroll in Mathematics 19A (completion of Mathematics 2B or 3 or Mathematics Placement Exam score of 40 or higher) or completion of Mathematics 19A or 11A, or Applied Mathematics and Statistics 11A, or Economics 11A.

Student Responsibilities

Students enrolled in this class are agreeing to the following:

  • Work turned in for quizzes and exams must be the result of individual effort. You can work on homeworks in teams, but each student is responsible for learning how to solve each homework problem.
  • Attendance to class is not mandatory, but you must attend one of the lecture sections each week. TAs will explain homework problems and hold bi-weekly homework quizzes at the beginning of section.
  • If any work claimed by a student to be his/her own is found to be shared with other students, that will be considered a violation of academic integrity and will be handled accordingly.
  • Students are also responsible for checking the class web page frequently for class material, updates, schedule changes, and assignments.


The grading system takes into account class participation, exams, homework quizzes, and the final. If you choose to attend discussion sections, your grade will be computed as follows:

  • Homework quizzes (30%): Every other week, closed book, closed notes
  • Midterm (30%) closed book, closed notes. Covers most of mathematical proof
  • Final Exam (40%) closed book, one page of notes. Covers all material

Exams and the final will be closed book, closed notes, with some allowance for one-page help notes for the midterm and final.

There are no curves in this class! Your effort determines your grade independently of how well other students do.

The grading scale for the class will be approximately: A+ (96%-100%), A (92%-96%), A- (88%-92%), B+ (84%-88%), B (80%-84%), B- (77%-80%), C+ (74%-77%), C (64%-74%), D (60%-64%), F (below 60%). I will use my discretion to deal with borderline cases. Class participation and extra effort will be taken into account.

Academic Integrity

In this course we encourage students to get involved in discussions about the class material in- and outside class. However, all work submitted for the class is to be understood by each student. It is fine to solve homework problems as a group, provided that each group member understands the answers she/he submits.

Students should be familiar with the University Academic Intergity Policies, violations of which will not be tolerated. Students who violate University standards of academic integrity are subject to disciplinary sanctions, including failure in the course accompanied by a report which will be part of the student's file, and suspension from the University.

If you have questions or doubts about the UCSC Academic Integrity policies, please see the instructor or the TA.


Our textbook is:
K.H. Rosen, Discrete Mathematics and Its Applications, Seventh Edition, McGraw-Hill, 2012.
ISBN 978-0-07-338309-5

The much-cheaper custom version of teh book is:
Martine Schlag, Discrete Mathematics, Seventh Edition, McGraw-Hill, 2013. ISBN 9781121564503

We will follow the textbook closely, but not necessarily in order.

CAUTION: We are using the 7th edition! There are options for acquiring the text:

  • Buy a new or used version of the 7th Edition from an on-line site or real bookstore.
  • Buy the custom version of the 7th Edition from the UCSC bookstore, which is MUCH cheaper. This is a softcover black and white version of the text with those chapters that we cover.

Syllabus The following list maps the topics that we will cover in class to the textbook sections and class dates. Remember this schedule will be modified as we make progress in this course. Check this page often.
  • April 2: Introduction to class, foundations of logic (Sec. 1.1)
    Class notes

  • April 4: Foundations of logic, application to logic circuits, propositional equivalences (Sec. 1.2, 1.3)
    Class notes, Sections 1.1, 1.2
    Class notes, Section 1.3

  • April 9: Logical equivalences (Sec 1.3). Sets (Sec 2.1).
    Class notes, Section 2.1

  • April 11: Sets and set operations (Sec 2.2).
    Class notes, Section 2.2

  • April 15--19: QUIZ WEEK
    Quiz 1 covers Sections 1.1, 1.2, 1.3, and 2.1.
    AVERAGE GRADE = 86/100
    Out of 154 students, 46 perfect scores (Wow!),
    81 scores with A or A+, 112 scores with B or higher, 7 no shows.

  • April 16: Predicates, quantifiers and rules of inference (Sec 1.4, 1.5, 1.6).
    Class notes, Sections 1.4, 1.5
    Class notes, Section 1.6
    Doc camera notes

  • April 18: Mathematical proof (1.7)
    Class notes
    Doc camera notes

  • April 23: Mathematical proof (1.7, 1.8)
    Class notes
    Doc camera notes

  • April 25: Conclusion of mathematical proof.
    Functions, sequences, summations and products (Sec 2.3, 2.4)
    Class notes
    Doc camera notes

  • April 29-May 3: QUIZ WEEK
    Quiz 2 covers Sections 2.2, 1.4, 1.5, 1.6, 1.7.
    AVERAGE GRADE = 76/100
    Out of 154, 41 perfect scores (awesome!!!),
    58 scores with A or A+, 78 scores with B or higher, 9 no shows.

  • April 30: Mathematical induction (Sec 5.1).
    Class notes

  • May 2: Induction, strong induction (Sec 5.1, 5.2)
    and recursive definitions (Sec 5.3).
    Class notes
    Document Camera notes

  • May 7: Recursive definitions (Sec. 5.3). Counting methods (Sec 6.1)
    Class notes
    Document Camera notes

  • May 9: Counting methods (Sec 6.1) and Pigeonhole principle (Sec 6.2)
    Class notes

  • May 13--17: QUIZ WEEK
    Quiz 3 covers Sections 1.8, 2.3, 2.4, 5.1, 5.2.
    AVERAGE GRADE = 65/100
    Out of 153, 16 perfect scores (great job!!!)
    27 scores with A or A+, 49 scores with B or higher, 11 no shows.

  • May 14: Counting methods (Sec. 6.2, 6.3, 6.4, 6.5)
    Class notes

  • May 16: Conclude counting methods (Sec. 6.5). Recurrence relations (Sec. 8.1, 8.2)
    Class notes
    Doc cam notes

  • May 21: Recurrence relations (Sec. 8.2), probability (7.1, 7.2).
    Class notes
    Doc cam notes

  • May 23:
    Midterm Exam (Covers Sections 1.1 to 6.2).
    Closed book, closed notes
    AVERAGE GRADE = 76/100
    Out of 153, two scores of 110 and 16 scores of at least 100 (great job!!!)
    36 scores with A or A+, 70 scores with B or higher, 3 no shows.

  • May 27--31: QUIZ WEEK
    Quiz 4 covers Sections 6.1 to 6.5 and 8.1.
    AVERAGE GRADE = 64/100
    Out of 153, 8 perfect scores (nice!!)
    16 scores with A or A+, 42 scores with B or higher, 17 no shows [I assume previous quiz grades were awesome? :-) ]

  • May 28: Probability (7.3, 7.4).
    Class notes (continued from May 21)

  • May 30: Probability (7.3, 7.4).
    Class notes

  • June 4: Applications:
    Countability of infinite sets and proofs by diagonalization (Sec. 2.4)
    Number theory, division, primes, congruences (Sec. 4.1 to 4.3)
    Algoritms, complexity [only in hard-copy textbook]
    Boolean algebra (Sec. 12.1 to 12.4)
    Class notes

  • June 6: Short review
    Class notes from doc camera

  • June 11 (Tue): FINAL EXAM (4:00-7:00 PM)
    Covers all material up to May 30, but examples of proofs are fair game.

Requesting Academic Accommodations

If you would like to request academic accommodations due to a disability, please contact the Disability Resource Center, 146 Hahn Student Services, (831)459-2089 (voice) or (831) 459-4806 (TDD/TTY). They can authorize specific accommodations for you in this class on an Accommodation Request Form. Please present this form to me early in the quarter so that we can discuss the accommodations you might need for class. You will need to see me again at least three weeks before each exam to arrange for testing accommodations.

Grades On-Line

You can now access your grades in this course via eCommons. You can login at with your CruzID.

Be advised that your password should be the CruzID Gold Password! Go to eCommons Documentation and Tutorials at:
or ask your TA for instructions on how to use the system.

Our course is called: CMPE-016 Applied Discrete Mathematics.