Syllabus for MTH 225 (Discrete Structures for Computer Science 1) sections 01 and 02 at Grand Valley State University, Fall 2015.

MTH 225: Discrete Structures for Computer Science 1 -- Fall 2015 Syllabus

Course Information

Instructor information

Course Content and Learning Objectives

Overview of course

Discrete Structures for Computer Science is a two-semester sequence that gives a comprehensive introduction to concepts from mathematics that are foundational to computer science. MTH 225 is the first course of this sequence and focuses on five main content areas:

In addition to attaining mastery in the content of the course as outlined above, a major goal of the course is for each student to learn to use computational thinking to solve problems. Computational thinking refers to an approach to problem solving using four stages:

  1. Decomposing a problem into smaller parts that can be solved easily;
  2. Pattern recognition among the parts of the problem that lead to insights about the main problem;
  3. Abstraction about the patterns that you see, in order to make conjectures about unifying solutions to the main problem; and
  4. Algorithm design for solutions that solve the main problem based on your abstractions.

Computational thinking is a concept that links mathematics and computer science, and it will be the main conceptual "glue" that holds the course together.

Learning objectives

A successful student in MTH 225 will, throughout the semester, demonstrate evidence that she or he has done all of the following. These are our foundational learning objectives and everything we do in the course points back to these:

  1. Students will recall and use mathematical terminology, theorems, rules, algorithms, and notation from the five main content areas of the course correctly in all course work without syntactic, semantic, or logical error.
  2. Students will apply basic mathematical concepts from the five main content areas of the course to solve both theoretical and practical problems.
  3. Students will apply the basic concepts of mathematical proof (direct proof, indirect proof, and proof by induction) to analyze written proofs and construct new proofs of their own.
  4. Students will describe the uses of mathematics as a way of knowing in computer science and mathematical proof as a way of establishing knowledge in math and computer science.
  5. Students will identify and describe connections between the mathematical content of the course (sets, counting, logic, proof, probability) and the elements of computer science (algorithms, data structures, programs).
  6. Students will use computers as a tool for engaging in computational thinking, particularly through the use of the Python programming language.
  7. Students will learn new technical content independently and practice skills and behaviors connected with effective self-regulated learning.
  8. Students will be active, caring, and productive contributors to the class learning community.


Expectations for MTH 225 students

All students in MTH 225 are expected to agree to the following terms as part of the MTH 225 learning community:

A sign of your agreement to these terms will come through a contract that will bear your physical signature, signed during the first week of class.

Fair Warning: This is not a lecture-oriented class or one in which mimicking prefabricated examples will lead you to success. You will be expected to work actively to construct your own understanding of the topics at hand, with the readily available help of the professor and your classmates. Many of the concepts you learn and problems you work will be new to you and ask you to stretch your thinking. You will experience frustration and failure before you experience understanding. This is part of the normal learning process. Your viability as a professional in the modern workforce depends on your ability to embrace this learning process and make it work for you. You are supported on all sides by the professor and your classmates; this is why we will frequently refer to our class as a "learning community". But no student is exempt from the process and the hard work it entails.

Expectations for the professor

Just as each student is held to expectations of behavior, you are entitled to hold me (Prof. Talbert) to the following expectations as well:

Student Work in MTH 225

Overview of MTH 225 work and assessment

Your main goals in the course are to learn as much as you can about discrete mathematics, and to become fluent in computational thinking and its use in applying basic content to solve new problems. Part of my job in the course is to assess how well you are attaining these goals. The work you will do in the course does two things: First, your class work serves as opportunities to learn; second, the results of your work provide evidence of your mastery of course content and problem solving skills.

Your final course grade will indicate the level to which this mastery has been attained. You will earn your course grade by completing tasks that lead to certification in our five main content areas (sets, counting, logic, proof, probability) at different levels, as well as certification that you have been a productive member of the MTH 225 learning community. The higher the grade you wish to earn, the more tasks you will need to complete and the higher the levels of those tasks.

Each of the tasks is evaluated on the basis of whether it meets professionally acceptable standads of quality. None of the work you will do in the course has a numerical point value. Instead, each time you submit work, it will receive an evaluation of whether the work meets the appropriate standard or does not along with extensive feedback on the work itself if the standard is not met.

The specifications used to evaluate your work are given in detail in the separate document Specifications for Student Work in MTH 225. Please read this document carefully and review it before turning in work, so you can evaluate your own work before submission and make adjustments. We will use this document in class through the semester to do activities in which we will evaluate student work samples, to give you practice in working with the specifications.

Please note the following carefully:

The next two subsections detail what it means to certify as a member of the MTH 225 learning community, and what it means to certify your mastery on course content.

Certifying as a member of the learning community

One of our main course goals is for each student to be an active, caring, and productive contributor to the class learning community. This involves doing your part to prepare well for class, contributing to group activities in class, taking the lead on occasion in those group activities, and doing other things in and outside of class to help others learn.

There are three kinds of work students do as preparation for class or as in-class work:

Please see the course calendar for a schedule of Guided Practice and Homework A and to get a feel for how the course meetings flow on a daily basis.

Guided Practices and Homework A are assessed on a two-level rubric of either Pass or No Pass. A Pass is given to work that is complete, submitted on time, clearly presented, and shows a good-faith effort to be right on each item. Mathematical correctness is not one of the criteria for grading; in fact these items are intended specifically to give a safe space to make and learn from mistakes. Complete specifications for your work in these three activities are given in the Specifications document mentioned above.

Each student will need to certify that they have done acceptable work as members of the MTH 225 learning community. The following may be used as acceptable evidence for contributing to the MTH 225 Learning Community:

Certification can be at Level 1, indicating baseline acceptability as a learning community member; or at Level 2, indicating contributions and leadership above and beyond the minimum acceptable level. The requirements for certification at these levels are as follows:

To certify at this level: Do the following:
Level 1 Complete 40 total instances of Learning Community activities, including at least one (1) Passing individual class presentation of Homework A.
Level 2 Complete 60 total instances of Learning Community activities, including at least two (2) Passing individual class presentation of Homework A.

Being the lead presenter on your group's Homework A presentation counts as two activities: being part of the group, and being the presenter.

Students who complete 80 or more instances of Learning Community activities will be awarded an extra token (see below).

(Note: Changes to the above table were voted in by the class on October 26.)

Certification and Recertification on course content

At various points in the semester you will be asked to certify your mastery of the content by completing what we call learning bundles. There are five learning bundles, one for each main topic in the course (sets, counting, logic, proof, probability). Additionally, you may certify on each bundle at two skill levels: Level 1 certification indicates that you have attained baseline competency in the topic, while Level 2 certification requires mastery of more complex and higher-order tasks above and beyond those in Level 1.

To earn certification in a bundle, students must do a combination of the following:

(Change: Big Picture items were removed as a requirement for certification. They are now optional and earn 2 tokens.)

The requirements for certification on a learning bundle are as follows:

To certify at this level: Do the following:
Level 1
  • Attain Pass rating on Level 1 bundle assessment; and
  • Satisfy the Level 1 requirements on the bundle's Homework B set.
Level 2
  • Attain Pass rating on Level 1 bundle assessment; and
  • Attain Pass rating on Level 2 bundle assessment; and
  • Satisfy the Level 2 requirements on the bundle's Homework B set.

The class sessions that are scheduled for certification assessments are cumulative in the sense that new versions of each previous certification assessment will be available in case a student failed to certify on previous attempts. For example, during the first assessment session, students may take the Sets Level 1 and Sets Level 2 certification. If a student passes Sets Level 1 but not Sets Level 2, then she may retake Sets Level 2 at the second session, which will feature not only Sets Levels 1 and 2 but also Counting Levels 1 and 2. In this way, each certification assessment can be attempted multiple times until a Pass rating is earned. However, note: bundle certification assessments can only be attempted twice (that is, an initial attempt plus one reattempt) without cost; third and subsequent attempts require the spending of one token (below).

Please note that subsequent versions of certification assessments will be new versions, not identical copies, of the previous versions. The tasks that are assessed on each certification assessment are found in the Certification Tasks document posted on Blackboard.

Additionally, students will need to recertify their mastery on some of the bundles to ensure that they have retained their original mastery on course topics through the semester. Recertification is done via in-class assessments held during the last week of the semester and during the final exam period. Each bundle will have a recertification assessment at each level; these are shortened versions of the original certification assessments. Note in particular that MTH 225 does not have a final exam; the final exam period is merely a 100-minute session for those students who need recertification. Note also that there are no homework or Big Picture requirements for recertification; all one needs to recertify on a bundle at a particular level is to earn a Pass rating on that bundle/level's recertification assessment.

Note that the Probability bundle will not require recertification because of how late in the semester it will appear. Only initial certification is required for this bundle.

Revision of work

Any item that is assessed on the basis of mathematical correctness can be re-done if needed until an acceptable level of quality is reached. Those items are certification assessments, recertifications, Homework B, and Big Picture items. The standards for acceptability for all course work are detailed in the Specifications for Student Work document.

Revision and resubmission works as follows:

Guided Practice, Homework A, and class presentations may not be revised (because these are not assessed on correctness but rather completeness, clarity, and effort).

Limitation on certification attempts: Each bundle assessment may be attempted twice without penalty. This is to encourage each student to take the bundle assessments as seriously as possible and to study hard for each one. Third and subsequent bundle assessments may be taken by spending a token (below).


To give students flexibility in the work in the course, each student begins the semester with five tokens (vritual currency) which can be "cashed in" for modifications to various deadlines and class policies. Tokens may be used for the following:

Use Tokens required
24-hour deadline extension on a Homework B assignment or Big Picture item (usable only once per assignment; may not be "stacked") 1
Resubmission of Homework B or Big Picture item rated at Repeat 1
Third or subequent attempt on a bundle assessment 1
"Free" Pass on a single Homework A or Guided Practice 2
"Free" Pass on an individual Homework A presentation 4
Submission of Homework B or Big Picture item more than 24 hours past deadline (but no more than one week past deadline) 5

Other uses for tokens suggested by students will always be considered.

Basis for Grading

Basic grading system

All of the aforementioned work is evaluated without points, using a Pass/No Pass, Pass/Repeat, or Pass/Repeat+/Repeat scale. To earn a particular course grade, you must earn Pass ratings on a certain number of level of course tasks. Generally speaking, the higher the grade you wish to earn, the more tasks and the more difficult those tasks you must complete at a Pass level.

Specifically, here are the requirements for grades of C, B, and A:

Put differently:

The conditions for grades lower than a C are as follows:

Use of the Probability bundle: There is no recertification offered on the Probability bundle. Therefore this bundle may not be used as an "elective" learning bundle for grades of C or B.

Grading system for plus/minus grades

Plus/minus grades are awarded for completing requirements at a level that falls in between the basic letter grades of A, B, C, D, and F. The table below gives the requirements for all possibl course grades including plus/minus grades:

Grade L1 cert L1 recert L2 cert L2 recert Learning Community level
A 5 4 4 3 2
A- 5 4 3 3 2
B+ 5 4 3 2 2
B 5 4 2 2 2
B- 5 4 2 1 2
C+ 5 4 1 1 1
C 5 4 0 0 1
C- 4 3 0 0 1
D+ 3 3 0 0 1
D 3 2 0 0 1

Note that GVSU does not award grades of A+ or D-.

Summary of grading assignment system

Notes about this grading system

Our grading system has several distinct advantages for you, the student:

A recent student commented about this grading system: ​“This class was not the easiest one that I had this semester, but it was definitely the least stressful because of the grading system.”​ I hope that it promotes a "client-consultant" relationship between you and me, in which we are working together to create a learning experience for you that is positive and productive.

The main downside of this system is that it can be complicated. Most students find it to be so, at first -- but as the semester unfolds, the logic of the grading system becomes much more evident. I will provide you with tools to track your progress through the course to help make it easier. And if you have any questions or concerns about the system, please let me know.

Other Course Policies

Policy on student communication responsibilities: Communication in the course takes place through three primary means: the course calendar, Blackboard announcements, and GVSU email.

Each student is responsible for communicating responsibly with the professor and other students and for keeping of all information flowing through the course.

Important dates: Please note these important calendar items (which are included on the course calendar):

Attendance and makeup policy: Missing a class meeting means that you are forfeiting your involvement in class activities, particularly Homework A presentations. If you know you are going to miss class, you may give your Homework A to another student to turn in for you; but you may not receive a makeup on presentations of Homework A, and you may not submit Homework A after class. Homework A writeups also are not accepted if the student forgets to bring them to class. Since the requirements for Learning Community certification are quit flexible, missing a few class meetings should not affect your grade since you can pick up the slack through other activities. Therefore makeups of class work are not offered. However, if you have missed several classes due to illness or other life situations and are afraid it is adversely affecting your grade, please contact me and I will be happy to discuss options with you.

Late submission policy: Deadlines on graded items will be enforced. You may purchase a 24­-hour extension on some items through the use of a token. Otherwise no late submissions will be accepted unless you have received approval prior to the deadline or can demonstrate that the lateness was unavoidable. Work that is late that does not have instructor approval is counted as a non­submission with no opportunity to revise.

Class cancellation policy: Class cancellations will be announced as soon as possible through email and through Blackboard. You will be responsible for monitoring both email and Blackboard for instructions. Note that cancellations of class meetings need not mean that class activities are cancelled; in some cases we may move the meeting online so that we don't lose a day. Again, monitor your email and Blackboard for instructions in such cases.

Inclement weather policy: In case inclement weather makes it difficult or dangerous to attend class, you may opt not to attend; if missing class does not affect your grade significantly (see "Attendance and Makeup Policy") then you can simply miss class. Otherwise please contact me for further discussion. Note that the decision not to attend class because of weather does not automatically entitle a student to a makeup of missed work.

Significantly incomplete work policy: Work that is submitted that contains (in the professor’s best professional judgment) significant omissions, or work that does not represent a good­-faith effort at completion will be marked as a non­submission. Unless the student submits complete work before the 24­-hour deadline extension, the work will be treated as a non­submission without the possibility of revision.

Academic honesty: Academically honest work by a student is work that authentically reflects the student’s understandings, however incomplete, of the work being done. Grand Valley State University’s academic honesty­ and integrity policy is found in Section 3.1 of the GVSU Student Code, found here: Each student has the responsibility for being familiar with this policy and abiding by it. Please note that violations of the Student Code will be pursued vigorously. The minimum penalty for plagiarism or inappropriate collaboration is a non-Passing mark on the affected assignment and an elimination of any further chances to revise the work. In especially egregious cases, the penalty can be significantly more severe, up to and including automatic failure of the course and possible suspension from GVSU. In addition, all violations of academic integrity will be reported to the Dean of Students and the Dean of the College of Liberal Arts and Sciences.

Collaboration: Each item of work has different parameters for the amount of collaboration that is allowed.

For students with special needs: Grand Valley State University (GVSU) is committed to providing access to programs and facilities for all students, faculty, and staff. GVSU promotes the inclusion of individuals with disabilities as part of our commitment to creating a diverse, intercultural community. It is the policy of GVSU to comply with the Americans with Disabilities Act as amended by the ADA Amendment Act (2008), Section 504 of the Rehabilitation Act of 1973, and other applicable federal and state laws that prohibit discrimination on the basis of disability. GVSU will provide reasonable accommodations to qualified individuals with disabilities upon request. If there is any student in this class who has special needs because of learning, physical, or other disability, please contact me (Prof. Talbert) or the Disability Support Services office (200 STU, 616–331–2490).

Updates to this syllabus: The syllabus is subject to change if amendments and additions are warranted. All changes will be communicated appropriately to the class in this case, and changes will be made to the electronic version of this syllabus that is located on GitHub and linked to the Blackboard site.

Instructor biographical sketch

I am an Associate Professor in the Mathematics Department here at GVSU. I came to GVSU in 2011 after spending 10 years (2001--2011) on the faculty at Franklin College in Indiana, and then 4 years (1997--2001) at Bethel College in Indiana. I started teaching when I was a junior in high school, giving private trumpet lessons and working as a tutor in math, statistics, and Latin. I first taught as a classroom instructor while in graduate school in 1994.

My undergraduate degree is a B.S. in Mathematics from Tennssee Technological University, and I earned my M.S. and Ph.D. degrees in Mathematics from Vanderbilt University. At Vanderbilt, I was a Master Teaching Fellow at the Center for Teaching and won two teaching awards, the B.F. Bryant Prize for Excellence in Teaching (awarded through the math department) and the Outstanding Teaching Assistant award as the top teaching assistant at the university.

Teaching is the most important part of my work at GVSU. Not only is teaching challenging and rewarding in itself, it also is the focus of much of my research at the moment in the scholarship of teaching and learning as well as many of my service opportunities on campus and off campus. Last year I was honored to receive GVSU's Pew Teaching with Technology Award as well as to be GVSU's nominee for Michigan Distinguished Professor of the Year.

My mathematical research was formerly in a field called algebraic topology which is a hybrid of geometry and abstract algebra. These days, my interests have shifted to the scholarship of teaching and learning and to areas that are at the intersection of mathematics and computer science -- areas such as cryptography, theoretical computer science, and functional programming.

Here at GVSU, in addition to my teaching opportunities and research projects, I am the chair of the Faculty Teaching and Learning Center Advisory Committee and of the Math Department's Student Affairs Committee, and I serve as the Math Department's instructional resources coordinator which involves managing all the department's classroom technology assets such as computers, software, and tablet devices.

Outside of GVSU, I serve frequently as a speaker and consultant for educational groups wishing to learn more about effective teaching and learning. This semester I will be giving keynote presentations and workshops in Kansas City, MO; Kingston, Jamaica; and two online events.

I am originally from middle Tennessee, near Nashville, and I have moved steadily northward my entire life. I currently live in Allendale (near Allendale Middle School, about 5 miles from campus) with my wife, three kids (ages 6, 9, and 11) and three cats. My hobbies include technology of all sorts, playing on the Wii U with my kids, running, cycling, soccer, American football, and reading.

For more information about me and what I do, please visit my website at and my blog at