Computer science is not about machines, in the same way that astronomy is not about telescopes. There is an essential unity of mathematics and computer science.
-- Edsger W. Dijkstra
Welcome to MTH 325! I'm Dr. Robert Talbert, the professor for this course. I'm grateful you're here.
This syllabus contains all the information you need to navigate the course. The main document will be kept continuously up to date at this link. When you see blue- or purple-underlined text in the syllabus or any other document, it's a clickable link. For example, click here for a cat video. A PDF version of the syllabus is available upon request.
This document is meant to be read once, then searched as needed. If you need to find something, the easiest way is to pull up this document, hit Control-F (Windows) or Command-F (Mac), and then do a search for the text you're looking for.
Course materials for MTH 325 are available on GitHub at https://github.com/RobertTalbert/discretecs. The current version is in the folder MTH325-Fall2024. Critically important documents will also be on Blackboard in the Course Documents folder.
This course is subject to the GVSU policies listed at http://www.gvsu.edu/coursepolicies/.
I (Prof. Talbert) reserve the right to adjust this syllabus as needed and will notify you of any changes through Blackboard.
Class meetings: Section 03 meets from 11:00-11:50am, in MAK A1161 on Monday and in MAK D2123 on Wednesday and Friday. Section 04 meets from 12:00-12:50pm MWF in MAK D2329.
Instructor: Robert Talbert, Ph.D., Professor of Mathematics. Office: MAK C2513. Email: talbertr@gvsu.edu. Phone: (616)331-8968. Be sure to read my availability policy below.
Drop-in hours: 2:00-3:00pm MWF and by appointment. Click here to set up an appointment: https://calendly.com/robert-talbert/mth-325-student-appointment
Webpage: The course Blackboard site is at http://lms.gvsu.edu. A Course Page, containing a summary of links to important documents and a record of class activities, is at this link.
Resources: The Course Vault is a wiki containing articles for each of the major concepts of MTH 325 (and MTH 225) and will serve as our primary "textbook": https://publish.obsidian.md/discretecs Other resources, such as video content and instructional websites, will be provided as needed. There is no required textbook, but the online text Discrete Mathematics: An Open Introduction is available for free as an optional supplement.
Technology requirements: It's highly recommended to have a laptop and access to a high-speed internet connection for work outside of class. You will need access to a basic handheld calculator for Checkpoint assessments in class. There is no preferred model of device. For in-class technology use, please see the policies in the "How we will use technology" section below.
MTH 325 is the sequel to MTH 225, where you learned some of the basic structures and concepts of mathematics for computer science: Logic, sets, functions, recursion and mathematical induction, and counting. In MTH 325, you'll extend these ideas to learn about four important and related ideas that are essential to computer science:
- Mathematical proof: Introduced in MTH 225, mathematical proofs are explanations of why a proposition about an observation is always true. In MTH 225 you learned one approach to mathematical proof, namely mathematical induction. In MTH 325, we expand on induction and introduce several other forms of proof.
- Graphs: A graph is an abstracted data structure used to model a network. They are of central importance to computer science, and in MTH 325 you'll learn how to apply them to real-life networks and determine information about those networks using mathematics.
- Trees and search: A tree is a special kind of graph that is encountered frequently in computer science, especially in different approaches to search algorithms and information systems, and like with graphs in MTH 325 you'll learn how to model real-life situations with trees.
- Directed graphs and relations: A directed graph (or "digraph") is a graph that has a direction to it, like an airline map or a system of rivers. One special use of digraphs is to model relations, which are abstracted forms of relational databases. In MTH 325 you'll learn the theory behind how and why these work.
After successful completion of MTH 325, you will be able to...
- Compute basic information about graphs, relations, and trees.
- Solve theoretical and applied problems involving applications of basic concepts of graphs, relations, and trees.
- Formulate computational problems in terms of graphs, relations, and trees.
- Construct a logical framework for a proof using mathematical induction, direct proof, proof by contraposition, or proof by contradiction.
- Analyze the structure and validity of a mathematical proof.
- Employ effective problem-solving skills in solving computational problems.
- Explain methods and solutions of computational problems in a clear way to a specified target audience.
- Demonstrate fluency in applying algorithms in the formulation and solutions of mathematical problems.
- Assess your own work in mathematical problem solving and apply feedback to make improvements to your own work.
During class meetings, active participation is essential. There will often be a brief (20 minutes or less) lecture over new concepts, followed by 20-30 minutes of activities of different types: problem solving sessions, computer-based lab work, electronic polling with discussion, and more. Your attendance and effort will be needed during every meeting of the class; without attendance and effort, it will be hard to succeed. Some class meetings are set aside for four Exams and makeups for those exams.
Before and after class meetings, the main activity is Homework. This is a combination of practice from the topics discussed in class and preview activities for the next class. Those preview activities will typically involve experimenting with an idea, and perhaps learning some basic content through video or reading. You are not expected to "teach yourself the material" -- these are just activities to introduce you to a new concept. But, the lectures in class will assume you have completed the preview activities so a good-faith effort to complete these each time is essential for your success in the course.
Outside of class meetings, other than Homework, you'll be given occasional Advanced Homework sets, typically every other week. These will contain more advanced problems involving applications of basic material learned in class. Since mathematical proof is a critical focus of MTH 325, you will also be completing proof problems during the semester; these will be posted and you will complete a selection.
Staying engaged in the course both in and outside of class meetings is crucial for success. You'll occasionally be given activities that promote positive engagement with the course, for example the Startup activities at the beginning of the semester. These and other engagement-focused activities earn Engagement Credits (like "experience points" in a game) and you'll be accumulating engagement credits throughout the semester.
You can ask a question about anything at any time. I am typically on campus MWF the entire working day with drop-in hours set aside especially for MTH 325 students from 2:00pm to 3:00pm MWF. Each of you is invited to drop in during those times, with any items you want to discuss, no appointment necessary. If you have a question outside those times, you can email those to me (talbertr@gvsu.edu) or set up an appointment at another time by clicking here: https://calendly.com/robert-talbert/mth-325-student-appointment
There are three main areas that contribute to your course grade:
- Mastery of basic skills;
- Application of those basic skills; and
- Engagement, effort, and participation
Mastery of basic skills: The basic skills of MTH 325 can be broken down into 14 sorts of tasks, which we'll refer to as Skills. A list of those 14 Skills is in Appendix A of this syllabus. Your ability to perform these tasks is measured by completing problems that demonstrate those skills. A sample of these 14 kinds of problems is given in this document. Five (5) of these are designated as Core skills. Part of your course grade is determined by how well you display mastery of these 14 problems/skills. For each problem/skill, I identify three levels of performance: Master, Proficient, and Beginner level. These problems appear on Exams that occur during the semester; four of these are planned and can be found on the course calendar. Each exam is cumulative: Exam 1 will contain problems for Skills 1-4; Exam 2 will contain problems for Skills 1-8 (with the first four problems being new variants of the ones from Exam 1); Exam 3 will have Skills 1-12; and Exam 4 skills 1-14. There will also be occasional short quizzes where you can attempt 1-2 problems of your choice; and the final exam in the course consists of new variants of all 14 problems.
I will record how well you do on each problem: "M" for mastery, "P" for proficient, and "B" for beginner and record the letter in Blackboard. Detailed rubrics for how those grades are determined can be found in the Standards for Student Work document. Your best attempt on a problem is kept, so if you earn an M on a problem on the first try, you do not need to reattempt it again at any point in the semester; but if you earn a P, you can try again at a subsequent exam or quiz, or on the final.
Application of basic skills: The basic skills can be applied in two different ways: real world applications and mathematical proofs.
Real-world applications appear on Advanced Homework sets which you'll receive roughly every other week. These include some basic and extended practice problems, and harder problems that involve applications. Each Advanced Homework is graded as a whole using a rubric found in the Standards for Student Work document, and in Blackboard we record either Success if the work meets the standards, or Retry if it does not.
We will maintain a running list of proof problems, added to on a regular basis as we learn more material, from which you can select a few to demonstrate skill with writing proofs. You'll take the ones you select, solve them, give them a nice writeup, and submit them on Blackboard for grading. Like Advanced Homework, proof problems are graded using a rubric found in the Standards for Student Work document, and in Blackboard we record either Success if the work meets the standards, or Retry if it does not.
The process of revising or resubmitting Advanced Homework or proof problems is given in detail below, in "How to revise or reattempt an assignment".
Engagement, effort, and participation: There are several ways to demonstrate engagement with the class.
- The foremost is Homework, which as described above is a brief assignment given after a class meeting that contains a review of the lesson and a preview of the next lesson. Completing Homework regularly is critically important for success in MTH 325. Homework is graded either Success or Incomplete on the basis of completeness, effort, and timeliness. See the Standards for Student Work document for details.
- Other activities will appear in the class that will let you earn engagement credits. Attending a class meeting earns one engagement credit. Other activities will have different engagement credit values. By completing these activities, you'll accumulate engagement credits through the semester.
Your basic course grade -- A, B, C, D, or F without plus/minus modifiers -- is earned by completing a minimum number of requirements in each of the main types of assignments in the class, using the table below. The numbers in the "Skills" column refer to the number of Master ratings you earn; Proficient and Beginner do not count in this total. The numbers in Advanced Homework, Proof problems, and Homework refer to the number of Success marks earned. We are planning on a total of 8 Advanced Homework sets, between 8 and 12 Proof problems, between 22 and 25 regular Homeworks, and a total of 70 engagement credits; if these numbers should change during the semester, the table will be updated accordingly.
| Grade | Skills | Advanced Homework | Proof problems | Homework | Engagement Credits |
|---|---|---|---|---|---|
| A | 13 | 6 | 5 | 18 | 60 |
| B | 10 | 4 | 2 | 16 | 50 |
| C | 7 | 2 | N/A | 14 | 40 |
| D | 5 | N/A | N/A | 10 | 20 |
Your course grade is the highest grade for which all the requirements in its row are met. A grade of "F" is given if not all of the requirements for a "D" are met.
Mastering the core: Failing to earn Master rating on all five Core skills will result in a one-letter grade penalty (for example B- to C-).
Final exam and plus/minus modifiers: The final exam in the course will be one more exam where all 14 skills are present (that is, a duplicate of Exam 4 with new variants of each problem). A "plus" is added to your basic grade by taking the final exam and doing Master-level work on all 5 Core skills plus any 2 others, if you have already done Master level work on those skills. (If you haven't, then the final exam will be your first Mastery of those skills.) A "minus" grade is given if either you don't take the final exam, or you take it but fail to do "Master" level work on all 5 Core skills. (So, the final exam's impact on the course grade is only to determine plus/minus modifiers.)
Borderline cases: Borderline cases in the grade table (for example, completing all requirements for a grade except for one) will be decided using Homework completion and engagement credits. So it's to your advantage to complete all Homeworks and earn as many engagement credits as you can. You may be assigned a course grade higher than what the syllabus indicates if I believe it's warranted by your Homework and engagement; you will never be assigned a course grade lower than what the syllabus indicates.
What this way of determining grades says, in regular language, is that:
- If you master half the skills in the class including the five Core skills, provide minimal but nonzero evidence of being able to apply those to real world problems, and stay reasonably engaged in the class, you can expect a grade of "C".
- Earning an "A" on the other hand means you have mastered all, or all but one, of the skills in the course including the five Core skills, provided consistent evidence that you can apply those basics, written several good mathematical proofs, and have stayed consistently engaged and prepared for class.
This way of doing grades is unusual, but it has some advantages:
- Almost every assignment can be revised or reattempted if you need to improve your work (see the next section below), and once you have demonstrated Mastery on a problem, homework, or proof you do not have to revisit it again in the course (except skills, at the final exam). It's possible that if you do well on the Exams, you will only need to work a fraction of the final exam. Many times, students just opt out of the final altogether if they have strong Exam performances (and don't care about having a minus).
- If you have a shaky performance on an assignment early in the semester, you have time to practice and improve, and those early performances don't hurt you.
- Because your grade is earned by accumulating successes, your grade in the course never goes down -- it only stays the same or goes up.
- It is easy to track your grade and find where you stand since there's no math involved other than adding up successes.
The main downside of this way of doing grades is that it can be complicated, and it can seem weird at first. We will take time to practice with the system; most students "get it" after a couple of weeks of use. But, if at any time you are uncertain about how you are doing in the class, please ask me and I'll be happy to clarify your situation.
Almost every assignment in the class can be revised or reattempted if you are not happy with the results, and you are not penalized for any reattempt or revision. The exception to this rule is Homework and items earning engagement credits; there are no reattempts or revisions allowed on Homework since it is partially a preview of an upcoming class, and since it's graded only on completeness, effort, and timeliness it is very easy to get a Success mark every time. Likewise, engagement credit items are typically one-off items that you either complete or don't complete, so revision doesn't apply.
For the other assignments in the class, here are the details for how this works:
- Skills/Exam problems: Exams are cumulative, so each exam contains new skills/problems as well as new variants of older ones. If you attempt a skill/problem and do not earn Master on it, you can reattempt it at the next exam or at a quiz given in between exams.
- Advanced Homework: You can revise and resubmit each Advanced Homework set once (for a total of two attempts). Your initial attempt will get verbal feedback on it, and you can use the feedback to make any corrections or improvements that are called for. Advanced Homework is submitted on Blackboard in an assignment area; revisions are simply submitted to the same assignment area.
- Proof problems: You can revise and resubmit attempts at proof problems as many times as needed but no more than three total submissions per week including initial submissions. So for example, in a given week you can submit two new proofs and a revision of a previous one; or three revisions; or three new proofs; and so on. Like Advanced Homework, revisions of proofs are uploaded to Blackboard in the same assignment area as the original submission.
For the purposes of revision, a "week" is defined to run from Sunday through Saturday, like on a calendar.
To keep the grading process operating efficiently we will place the following restrictions on revision and reattempts:
- As mentioned above, Advanced Homework sets can be revised only once; proof problems can be revised as needed but there is a limit of three total submissions per week.
- Advanced Homework and some proof problems will come with a deadline for initial submissions. You must submit a complete, good-faith effort on the assignment prior to the deadline in order to be eligible to revise or resubmit it. Examples of situations where revision would not be allowed include the following:
- The assignment is not submitted at all before the deadline (In other words you cannot "revise" an assignment you did not turn in)
- The assignment is submitted but some problems are skipped or omitted either partially or entirely, or includes responses saying something like "I didn't know how to do this part" but no signficant attempt at a solution
- The assignment is submitted but the work has significant issues or errors throughout -- so much so that it is impossible to tell if there is any understanding of the concepts.
- Revisions of Advanced Homework sets also have a deadline. No revisions are accepted past that deadline.
- No revisions or reattempts on any item are allowed after 11:59pm ET on Sunday, December 8. This is the beginning of the last week of classes, and no revisions or reattempts are allowed after that point so that the queue of items to grade can be cleared prior to the final exam.
We will use digital tools, including computer software and artificial intelligence tools, regularly in MTH 325 as tools for learning. MTH 325 students are not only encouraged to use technology in this way, but are expected to do so. However, these tools can also be a strong distraction to your engagement, so we'll use them with limits.
During class meetings that are not Exams, please have all technology including laptops and phones put away, in your bags and not out on the desks. Having technology out during a class meeting at any other time or under any other condition will result in a request to put it away first, then a loss of engagement credits if that request is not satisfied. There are three exceptions to this rule: (1) you can have technology out if specifically instructed to; (2) you can have technology out if you have given me a memo from Student Accessibility Resources (SAR, formerly known as Disability Support Resources (DSR)) that says you can use it in class; and (3) the technology is an e-ink notebook device (for example, the Remarkable tablet) that has no web browser or communication capabilities.
During Exams, you are allowed the use of a scientific or graphing calculator, or a smartphone calculator app if the phone is in airplane mode. No other technology will be allowed (or necessary) on exams.
Outside of class, you are generally free to use technology without restrictions, unless restricted in the instructions on an assignment. In particular, the use of generative AI tools (ChatGPT, etc.) can be highly beneficial but also highly disruptive to learning; see "Academic Integrity Policy" below for more.
You should be proficient in the basic technology skills listed at this GVSU policy page. This list is for online and hybrid courses, but it applies to our class as well. If you need help at any time with those skills, please ask me or a classmate. You will also need basic proficiency in the Python programming language; completion of CIS 162 is sufficient. If you need tutorials on Python, please let me know.
Tech support: I (Talbert) am not able to provide tech support since I lack the skill and permissions to fix all possible problems. Do not contact me first when tech problems arise. Instead, contact the appropriate person or office listed below, then let me know the situation:
- For help with Blackboard: Email the Blackboard Help Desk at bbadmin@gvsu.edu or call (616)331-8526. For hours of operation and more information see http://www.gvsu.edu/elearn/help.
- For help with the GVSU network, email, or printing: Email the GVSU IT Help Desk at helpdesk@gvsu.edu; or call (616)331-2101 or toll free (855)435-7488. For hours of operation and more information see https://www.gvsu.edu/it.
- For help with your computer: Try the GVSU IT Help Desk (above) or contact your device's manufacturer or a computer store.
- For help with any other technology: Seek out the help documentation in the tool you are using, or do a targeted Google search. Ask a classmate or me if you are unable to resolve the issue.
If technology issues prevent submitting work: If you have contacted an appropriate source of help and an issue still persists that prevents you from turning in work in the usual way (for example on Blackboard), you are expected to take alternative measures to get your work turned in on time. For example, if Blackboard is offline, send an email with an attachment. Then, submit the work using the normal means later.
TL;DR: When you submit work on an assignment in this class, it must be your ideas and your voice, and not someone else's or those of an AI. Anything else is subject to strong penalties that are required by the university.
This course is subject to GVSU course policies and the GVSU student code. This document establishes guidelines and expands and clarifies these policies with respect to all work done in MTH 325 this semester. Every student is required to be familiar with these policies and the consequences of violating them.
The student code defines academic misconduct as "any action or behavior that misrepresents one’s contributions to or the results of any scholarly product submitted for credit, evaluation, or dissemination". These include:
- Cheating: Attempting to use materials, information, or aids that have not been authorized by the instructor for academic work.
- Collusion: Unauthorized collaboration with another person in preparing academic assignments offered for credit, and collaboration with another person to commit a violation of any section of the rules on academic misconduct. Please note: In MTH 325, generative AI tools such as ChatGPT are included in the definition of "person".
- Dual submission: Submitting work that has been previously graded, or is being submitted concurrently to more than one course, without authorization from the instructor of the class to which the student wishes to submit. (This especially applies to those who are repeating MTH 325.)
- Plagiarism: Appropriation of, buying, receiving as a gift, or obtaining by any means material that is attributable in whole or in part to another source without any indication or citation of the original source, including words, sentences, ideas, illustrations, structure, computer code, and other expression or media, and presenting that material as one’s own academic work being offered for credit or in conjunction with a program, course, or degree requirements.
Please note that this is not a complete list; and note that the Student Code considers enabling others to engage in academic misconduct to be another form of academic misconduct.
In MTH 325, when you submit an item for grading, it must represent your ideas and be written in your voice, however flawed those may be. Your work cannot significantly consist of ideas or wording from another person or from an AI tool. Specific guidelines for each form of assignment are:
- Exam problems: These are completed on paper during a class meeting. No collaboration is allowed, and no notes are allowed.
- Advanced homework and Proof problems: Sometimes these are extensions of simpler problems that we do in groups during class, and you can use the results of that collaboration. Otherwise, you are allowed to consult with another person or an AI tool, if the issue pertains to terminology used in the problem, or very high-level discussions about what the problem is asking for. But no collaboration with people or AI is allowed on any question or strategy that involves actually solving the problem. A rule of thumb is: Collaboration or AI use intended aimed at "How do you solve the problem" questions, is off limits.
- Homework and engagement credit items: You're allowed, actually encouraged, to collaborate freely with others on these as long as you are obeying the general rule that the work you turn in is your ideas and your voice. If there is ever an exception, you'll be told in advance.
Academic misconduct is a serious matter that carries stiff penalties from the university. If I suspect that an item of work breaks the "your ideas/your voice" rule, I will first discuss it with the student turning the work in. If I determine that there was academic misconduct, the matter will go to the Office of Student Conduct and Conflict Resolution which has a process for handling these issues. The penalties can be quite severe, in some cases resulting in failure of the course or even suspension from the university.
Fortunately, however, our grading system makes academic dishonesty unnecessary and easily avoidable because of our revision and reattempt policy. Simply turn in work that is a good-faith effort at a complete and correct solution to the problems on the assignment; if your work doesn't meet our standards, you'll be given feedback and a second chance. There's no need to engage in academic misconduct with that system in place.
Instructor availability: Email (talbertr@gvsu.edu) is the best way to reach me with a message outside of class meetings. All messages needing a response will receive one by the end of the next working day (that is, Monday through Friday). Emails sent on Fridays will get a response by the end of the following Monday. I typically check email twice during the working day (early morning and late afternoon) and do not check email after 5:00pm, before 7:00am, or at any time on weekends. If you send a message during those times and your message needs a response, you will get one promptly when I am back at work. But in particular, please note that messages in the evenings and on weekends will not typically get an immediate response.
Announcements and email: You'll receive an announcement packet on Blackboard, each week on Sunday, with plans for the week, a list of due dates, and other announcements. Announcements may appear in between Sundays if there is something time-sensitive that needs your attention. Announcements are posted on Blackboard and copied to your GVSU email. Please check your GVSU email at least once a day, 7 days a week in order to stay up to speed with course happenings.
Attendance: Regular class attendance has been shown to correlate more strongly with student success in the class than any other variable. You are urged, and expected, to attend every class meeting unless it is physically impossible or inadvisable. Attendance at each class meeting earns 1 engagement credit, so by simply attending class you will earn most of the credits needed for an "A" in the course. Students who do not attend class consistently will be contacted to discuss their situations further. If you have a life situation that makes consistent attendance difficult, please bring it to my attention immediately so we can discuss your options.
Late work and makeups: The policies for late work and makeup work are indicated below. If you have a particular life situation that makes it difficult to meet deadlines consistently, please let me know and we'll talk about it.
- Exams: These are done on paper in class meetings. If you miss an exam day, there are designated makeup days set aside on the calendar for makeups. No other makeups are allowed.
- Advanced Homework: These come with a deadline both for the initial submission and for revisions. Initial submissions are not allowed after the initial deadline; revisions are allowed at any point up to, but not beyond, the revision deadline.
- Proof problems sometimes have a deadline for initial submissions. Like Advanced Homework, no initial submissions are allowed past that deadline. But, some proof problems will be deadline-free; and there is no deadline on revisions for any proof problem other than the last-call deadline of Sunday December 8.
- Homework and engagement credit items may not be submitted after their deadlines. (Some engagement credit items may not have deadlines in the first place.)
Contingency plans for remote instruction: In the event that we need to switch to remote instruction, class meetings will take place on Zoom, and the link will be shared in a course announcement and on the Class Page. If that day happens to be an exam day, we'll reschedule the exam and the focus of the class meeting will be determined at that time. Click here for the official university policy on remote instruction.
Gender identity and expression: If, for purposes of gender identity and expression, your official name (in Banner) does not match your preferred name, your name can be updated in Blackboard. Please contact the registrar's office to submit this request. The registrar's office will contact the Blackboard administrator to make the change and will also contact your professors to inform them that your name in Banner will not match the name in Blackboard.
Classroom and campus safety: I consider classroom and campus safety our shared responsibility. Please familiarize yourself with the classroom emergency placard, which contains important information that could prove useful should an emergency arise. Emergency situations could include a fire alarm, tornado warning, medical emergency, or hostile intruder, and our response might consist of evacuating MAK Hall in an orderly manner, moving as a group to a different location in the building, rendering assistance to a class member, or staying put and locking the classroom door. In all cases, I will provide clear instructions as to what you should do. Please make sure to have your primary mobile number listed in Banner so that you will automatically receive any campus alerts. Should you receive an emergency notification in class, notify me immediately.
MTH 325 can be a challenging course for a number of reasons unique to each student. It is almost certain that at some point, you will be challenged beyond your current ability level. (If this doesn't happen, I am not doing my job!) When it happens, the main thing to realize is that this is normal, it's not cause for alarm, and it doesn't indicate any deficiency in you as a person.
The best way to get help in the course is directly, by attending class and coming to drop-in hours. I am very happy to work with you one-on-one or in a small group on any difficulty you are having. Indeed this is my favorite part of the job.
Another good way to get help is to work with a small group of classmates either in class or out of class. We'll work in groups that rotate periodically, so you will get a good sample of people to work with. As long as you stay within the academic conduct bounds above (your ideas/your voice) then collaborating with other people is a great thing to do.
You can also use an AI tool to help with everyday issues. For example, if we are studying a concedpt and you need more examples than we have time to discuss in class, fire up ChatGPT and ask it for some more examples, or better yet, ask it for practice exercises.
For help with prerequisite concepts from MTH 225 or high school, consider visiting the Math Tutoring Center (http://gvsu.edu/tutoring/math/). Bring questions to any location about using technology, on methods and concepts, or on specific problems. All Math Center tutoring is free and available in person on both the Allendale and Pew campuses as well as on Discord.
I'm Robert Talbert, the professor for this course. I'm a Professor in the Mathematics Department and also hold an appointment in the GVSU President's Office. I have been teaching college math courses in different places for 32 years, and at GVSU since 2011. I have a Ph.D. in Mathematics from Vanderbilt University and a B.S. degree from Tennessee Technological University.
I was, at best, a thoroughly mediocre math student in school until my senior year of high school, when I had a teacher for Calculus who stopped trying to cram things into my head and instead showed me the basics, then backed off and let me work things out on my own, with support if I got stuck. (Basically, this is how I teach today.)
After spending my first two years of college as a Psychology major, I changed my major to math after a late-night dare from my roommate (long story) and, to my great surprise, I fell in love with the subject. I ended up going to graduate school to work in an obscure area at the intersection of abstract algebra and geometry, which seemed like pointless fun at the time but now turns out to have serious applications to data science and to the design of programming languages. I also discovered I loved teaching math to college students. So I went on to spend 14 years teaching in small liberal arts colleges before coming to GVSU in 2011.
Currently I teach a lot of MTH 225 and MTH 325, getting engineers and computer scientists to think like mathematicians. I also do research on making college teaching better and recently wrote a book about the kinds of grading systems you see in this syllabus. When nobody is looking, I am working on my data science skills and learning languages like R and Julia.
I've been a bass guitar player for over 25 years and play live regularly in the Muskegon/lakeshore area with the band Taproom Fix. You can learn more about my music and see some performance video at my Bandmix page.
I live in Allendale with my wife and 15-year old son (who wants to be a software engineer). I have an 18-year daughter who is a freshman at Wayne State University and a 20-year old daughter who lives on her own. I also love the outdoors and get out to run, walk, or hike when I can. You can read more about what I'm thinking and doing at my website, rtalbert.org, or Grading for Growth about alternative grading practices which I co-author with my GVSU colleague Prof. David Clark. I'm also on Twitter at @RobertTalbert and on LinkedIn. I will accept any connection request on LinkedIn from a student!
The spirit of this syllabus, and some of the wording, is taken from the syllabi of Prof. George McNulty who was a Mathematics professor at the University of South Carolina until his passing in 2023.
- (CORE) I can outline a proof by mathematical induction.
- (CORE) I can outline a proof using direct, contrapositive, and indirect approaches.
- (CORE) I can represent a graph in different ways, determine information (degree, degree sequence, paths of given length, etc.) about a graph using different representations, and give examples of graphs with specified properties.
- I can determine whether a graph has an Euler path or Euler circuit, and whether a graph has a Hamiltonian path or circuit.
- I can use a greedy algorithm to find a vertex coloring for a graph, and I can determine a graph's chromatic number.
- I can determine whether two graphs are isomorphic; I can give an explicit isomorphism if they are, and an explanation if they are not.
- (CORE) I can determine whether a graph is a tree and state information about it.
- I can use Prim's Algorithm and Kruskal's Algorithm to construct a minimum spanning tree for a weighted graph.
- I can use Dijkstra's Algorithm to find a minimum distance spanning tree for a weighted graph.
- I can execute a breadth-first and depth-first search in a graph.
- (CORE) I can represent a directed graph in different ways, and determine information about a graph using different representations.
- I can use the Floyd-Warshall algorithm to construct the transitive closure of a directed graph.
- I can determine whether a relation is reflexive, symmetric, antisymmetric, and/or transitive, and whether it is an equivalence relation; and if so, I can determine the equivalence class of a point.
- I can determine whether a relation is a partial ordering; if so, I can draw its Hasse diagram and identify maximal/minimal elements and/or greatest/least elements, if they exist.
A Google calendar for the class can be found at this link: https://calendar.google.com/calendar/u/0?cid=MWZiNGVmOTdkNmExOGQ1ZmFjNmQ2MTkwZjk1ZWZkMmFlN2FmZTIxMDViNTA3MjEyMDc1NWYyYTYzZDUyYmUzNUBncm91cC5jYWxlbmRhci5nb29nbGUuY29t
It is also embedded on Blackboard in the Course Documents folder. Please note, the calendar found on Blackboard in the "Calendar" tab at the top of the page is not the same as the Google Calendar and does not contain all the date-sensitive items in the course. Please use this Google Calendar as your official reference.
Exam and makeup dates:
- Friday, September 27: Exam 1 (Skills 1-4)
- Wednesday, October 16: Exam 2 (Skills 1-8)
- Friday, November 1: Makeup day for Exams 1 and 2 (Skills 1-8)
- Monday, November 18: Mini-Exam (Skills 9-14)
- Monday, November 25: Makeup day for Exam 3 and Mini-Exam (Skills 1-14)
- Monday, December 2: Exam 4 (Skills 1-14)
- Friday, December 6: Makeup day for Exam 4 and any other exam for which previous makeup days didn't work
- Wednesday, December 11: Final Exam
- Section 03: 10:00-11:50am
- Section 04: 12:00-1:50pm
Please note: Makeup days are only for students who were absent from the initial offering of the exam with an excused absence. They are not additional attempts open for all students. Students not needing a makeup are not required or expected to come to class on makeup days.
University dates:
- August 26: First day of classes
- August 30: 100% tuition refund deadline
- September 1-2: Labor Day recess, no class
- September 20: 75% tuition refund deadline, last day for CR/NC changes (5pm)
- October 15: Mid-term grades submitted
- October 21-22: Fall Break, no class
- November 8: Deadline to withdraw from class with a grade of "W"
- November 27-29: Thanksgiving Day recess, no class
- December 5: Classes end
- December 9-14: Final exams
- December 14: Semester ends
- December 16: Grades due (midnight)