Modern Computational Math

Course Information

Class Sessions

Monday, Wednesday, and Friday, 12:55–1:50pm in RNS 160R

Contact the Professor

If you have any question or concern about the course, email Prof. Wright at wright5@stolaf.edu or visit office hours (see above). If the hours above don’t work for you, just send Prof. Wright an email to arrange a meeting at another time!

Textbook

This course will use a draft of a new text, titled Exploring Mathematics from a Computational Perspective, by Richey and Wright, which will be made available electronically. Profs Richey and Wright are actively working on this text and appreciate all comments and feedback on the text throughout the semester.

Course Objectives

This course is about using computation to investigate mathematical ideas. Throughout the semester, you will:

1. Develop skill of using computation to investigate mathematical topics and ideas.
2. Use computational experiments to provide evidence for claims, stimulate questions, and formulate precise conjectures.
3. Develop/improve ability to work computationally in various programming environments, especially Mathematica and Python.
4. Develop mathematical problem solving skills applicable in a variety of theoretical and applied settings.

Software

The primary computational tools for this course will be Mathematica (available for St. Olaf students) and SageMath (available online). No prior programming experience is assumed, though a desire to learn through experimentation will be essential.

Grading

This course will use a system called specifications grading to evaluate your work. Rather than awarding points or partial credit, work is evaluated on whether it meets a clear list of specifications. Recognizing that these specifications set a high bar, an opportunity for feedback and revision is provided for the projects in this course. Furthermore, requirements for earning each particular letter grade are designed to be easy to understand and track throughout the semester.

Deliverables

This course will require four types of deliverables.

• Practice problems: These are small assignments designed to make sure you are keeping up with class sessions and textbook reading. These will be graded on a Satisfactory/Unsatisfactory scale. There will be approximately 60–70 practice problems throughout the semester
• Projects: The main component of this course will be five computational projects, which will build on computational work done in class. For each project, you will turn in a Mathematica or Python notebook containing your computation and explanations. Projects will be graded on the EMRN scale. After the professor provides feedback on each project, you will have one opportunity to revise the project. Due dates for projects and revisions will be announced in class and on this web site.
• Final Project: The final project will be an opportunity to investigate a topic in computational mathematics that goes beyond what we study as a class. These will be group projects, and will involve reading mathematical papers and doing computational experiments. Each project will result in a project notebook and a brief presentation, to be delivered during the final exam period (December 16, 1:00–3:00pm). The professor will provide feedback leading up to the final presentation session. Final projects will be graded on the EMRN scale.
• Challenge Problems: These are opportunities to demonstrate your ability as a computational mathematician. Challenge problems will involve independent computational investigation, resulting in your own observations, questions, and conjectures. They will be graded on the EMRN scale, with one opportunity for revision of each problem. The professor will offer many challenge problems throughout the semester. Individual challenge problems will not have due dates, but each student may submit up to two problems or revisions per week. Challenge problems will be accepted until the last day of class, December 9.

EMRN Grading Scale

Projects and challenge problems will be graded on the EMRN grading scale (adapted from here). Using this scale, work is evaluated as Excellent, Meets Expectations, Revision Needed, and Not assessable, as follows:

• Excellent: The work exceeds the expectations of the assignment. Communication is clear and complete. Mastery of the concepts is evident. There are no nontrivial errors. This work could be used as a classroom example.
• Meets Expectations: Understanding of the concepts is evident through correct work and clear, audience appropriate explanations. Some revision or expansion is needed, but no significant gaps or errors are present. No additional instruction on the concepts is needed.
• Revision Needed: Partial understading of the concepts is evident, but there are significant gaps that remain. Needs further work, more review, and/or improved explanations.
• Not assessable: Not enough information is present in the work to determine whether there is understanding of the concepts. The work is fragmentary or contains significant omissions. Or, there are too many issues to justify correcting each one.

Letter Grades

The letter grade you earn at the end of the semester will be determined by the criteria in the following table. To earn a particular letter grade, you must meet the requirements for that letter grade in all of the deliverable categories. This grading system is designed to align with the grading benchmarks in the St. Olaf Catalog.

Course Grade	Practice Problems	Projects	Final Project	Challenge Problems
A	90% satisfactory	3 E, 2 M+	E	4 M+
B	75% satisfactory	1 E, 3 M+, 1 R+	M+	1 M+
C	50% satisfactory	3 M+, 1 R+	M+	not required
D	25% satisfactory	1 M+, 3 R+	R+	not required

"Plus" grades will be awarded for completing the requirements of a certain letter grade, as well as one of the requirements for the next higher letter grade. For example, satisfying the requirements for a B in three deliverable categories, along with the requirement for an A in the fourth deliverable category, will result in a B+.

"Minus" grades will be awarded for completing all but one requirement for a particular letter grade, with the missing requirement completed as required for the next lower letter grade. For example, satisfying three of the four deliverable requirements at the A level, with the fourth requirement satisfied at the B level, will result in an A-.

For example, suppose you complete 85% of the practice problems satisfactorily, earn three Meets Expectations and two Revision Needed scores on the projects, complete 1 challenge problems, and earn a score of Excellent on the final project. This would satisfy the B criteria for practice problems, challenge problems, and the final project, but only the C criteria for projects. Your final grade in this case would be B-.

Prof. Wright reserves the right to adjust the letter grade requirements according to circumstances throughout the semester. (For example, if a project is cut due to schedule changes.) Any such changes will not increase the requirements for a particular grade.

Tokens

In recognition that sometimes we all need an extension or a second chance, this course will use a token system. Each student will start the course with 3 tokens, which may be spent as follows.

• Spend 1 token to turn in any deliverable up to three days late.
• Spend 1 token to turn in a project that you didn't turn in previously (until the last day of class).
• Spend 1 token for a second revision on any project, due one week after the first revision was graded.
• Spend 1 token to turn in a third challenge problem (or revision to a challenge problem) in a week.
• Spend 1 token to resubmit a set of practice problems (from one day of class), due one week after the problems were initially graded.

Tokens will be tracked using a text entry in the Moodle gradebook. There will be opportunities to earn extra tokens by attending MSCS colloquia or research seminars, as announced in class, and submitting a brief reflection.

Getting Help and Academic Integrity

Collaboration with peers is encouraged in this class. Discussing concepts and problems with other people is an important part of learning mathematics. Use of Mathematica and SageMath documentation and reference pages is also encouraged. However, collaboration and use of help resources must be done appropriately and with integrity.

Inappropriate “collaboration” includes copying answers from a friend, looking up homework solutions in online forums, asking an artificial intelligence to do your homework, any use of any other resource that does the thinking for you. Remember, the goals of this course are to develop and demonstrate your own skills of computational investigation and problem solving. You will not achieve these goals if you outsource your thinking to other experts (human or artificial). You will achieve these goals through time and effort spent solving topology problems.

Moreover, you must document what sources you use and what assistance you receive for work in this course. This could take the form of a simple acknowledgement in your homework assignment.

Because we want to develop codewriting skills in this course, the use of artificial intelligence to write code is not permitted without explicit permission from the professor. Debugging AI-generated code and confirming that it works as expected can be extremely challenging, and it's important to first develop your coding skills by writing code yourself. Toward the end of the semester, we will examine the use of generative AI in computational mathematics. Before we do that, however, we must first develop our own proficiency in codewriting and computational exploration.

Claiming someone else or something’s work as your own will earn you a failing grade on the work in question. Don’t do it. For more information, see the Academic Integrity section of The Book.

Prof. Wright is your primary resource for help in this course and is always happy to talk with you. The course teaching assistant will also hold drop-in help sessions two evenings per week, as stated at the top of this page. When you need help, or if you have any concerns about the course, please email Prof. Wright or visit his office hours. Furthermore, the Academic Success Center academic coaching and other services – email the Academic Success Center for more information.

In summary:

• It’s good to discuss course material and homework with classmates and the professor.
• It’s not good to ask someone (or an artificial intelligence) to do the homework for you.
• For each assignment, you must indicate what sources you consulted and what assistance you received (if any).
• If you have any questions or concerns about this course, talk with Prof. Wright.

Attendance

Attending and participating fully in class is important for learning and developing your skills in computational mathematics. If you don’t come to class, you’re missing out on the discussions and learning activities that takes place in class. For this reason, it’s crucial to develop consistent attendance habits from the beginning of the semester.

If you miss two consecutive classes without contacting Prof. Wright, he will reach out to the Dean of Students Office to make sure you're getting the support you need.

If you miss four classes (consecutive or not) without contacting Prof. Wright, he will require you to complete an additional form of engagement to show that you're making an effort to keep up with the course.

If you miss eight class sessions for any reason(s), and regardless of whether you contact Prof. Wright, he will encourage you to consider dropping the course. Eight class sessions amounts to almost one-quarter of all class sessions, which is an excessive amount of absences that severely detracts from your learning throughout the semester.

Final presentations will be given during the final exam period on Monday, December 16, 1:00–3:00pm. As you plan your holiday travel, make sure you will be able to attend the final presentations.

Strategies for Success

• Attend class faithfully and participate in class activities.
• Discuss the course material with other students. Mathematics is a collaborative activity! You will find that you will both learn from and teach your classmates. Make sure to acknowledge what assistance you receive on each assignment.
• Keep up with the assignments and projects. Start early—don’t wait until the last minute to get started!
• Don’t give up when your code doesn’t work. Writing good code often requires many revisions. Understand that mistakes are opportunities for learning.
• Ask questions! Experiment!
• When you encounter trouble, seek help!

Inclusivity and Access

Prof. Wright is committed facilitating a safe, caring, and inclusive learning community, respecting those of differing backgrounds and beliefs. As part of St. Olaf College, we aim to be respectful to everyone in this class, regardless of race, ethnicity, religion, gender, or sexual orientation. All students are capable of success in mathematics, and Prof. Wright aims to create an environment in which all can succeed. If you have any questions or concerns, don’t hesitate to talk with Prof. Wright.

If you have any concerns about access to course materials, or if English is not your first language and this causes you concern, please talk with Prof. Wright.

Health and Accommodations

Prof. Wright is committed to supporting all students. He recognizes that emotional, physical, or psychological experiences, both in and out of the classroom, have the potential to distract students from learning. If you have any concerns, please do not hesitate to contact the professor—he is available to listen and to discuss what resources may be available to you.

If you are feeling sick, please do not come to class—instead, email the professor. Face masks to prevent the spread of respiratory diseases are welcome in class. Please respect individuals who may choose to wear face masks. If the COVID-19 situation changes during the semester, we will adjust course policies as necessary, following the St. Olaf infectious disease guidelines. If you have any questions or concerns about community health with regard to this class, don’t hesitate to talk with Prof. Wright.

If you have an accommodation letter from the Disability and Access (DAC) office, please meet with the professor early in the course to discuss, plan, and implement your accommodations in the course. Otherwise, if you have or think you have a disability please contact the Disability and Access office.