Textbook

Our (required) textbook is the blue Analysis: With an Introduction to Proof (5th edition) textbook by Steven R. Lay. Pre-class reading and homework assignments are posted on Moodle Reading Forum.

Overview

This course aims to provide a transition from introductory calculus to higher mathematics. In particular, to develop skills in mathematical communication: oral, written, and typeset; to develop critical thinking skills; to introduce and practice techniques of mathematical proof.

Expectations

Definitions. By the end of each section, you are expected to:

state definitions accurately
identify whether or not an object meets the conditions of a given definition
give examples that satisfy a given definition
give examples that do not satisfy a given definition

Theorems. By the end of each section, you are expected to:

state theorems accurately
given a theorem, identify their assumptions and their conclusions
determine whether the conditions of a theorem do or do not hold in a given situation,
determine what a theorem does or does not imply in a given situation
recognize logically equivalent forms of a theorem
(by the end of the course) attempt to formulate and test conjectures

Proofs. By the end of the course, you should be able to:

recognize whether a proof is successful or flawed.
reproduce successful proofs written by others (for example, the textbook’s author)
write original, successful proofs (possibly with the assistance of a more experienced mathematician such as your myself)

Community. By the end of the course, you should be able to:

engage in discussions about mathematics by sharing questions, proposals, and insights
evaluate others’ contribution and respond constructively
present proofs (either your own or someone else’s) in front of an audience and address their questions and comments graciously

Assessments and grading

Tokens

Tokens are fake currency which may be spent on second attempts for in-class exams, take-home exams, and Overleaf writeups as well as late submissions:

Purpose	Token cost
Retake an in-class exam (if you pass fewer than 85% solutions on your most recent attempt) or take a late make-up exam	1 token
Resubmit an unsuccessful (or late) Overleaf final draft within 7x24 hours of deadline	1 token

You start out with three (3) tokens. You may use a token for any reason (sports and extracurricular activities, sickness, forgetting to wake up, etc). You don’t need to explain your reasons.

Note: If you attempt something more than once, only the outcome of the last attempt will be recorded.

Early make-up If you know in advance that you will have an excused absence, you may schedule an early make-up exam or quiz (with a 7-day notice) without using any token.

Assessments

In-class Presentations You will take turns presenting solutions to a list of problems. Your presentation does not need to be perfect, but it should show evidence of a serious effort. You should be prepared to answer questions from other students.

Note that if you let me know in advance that you cannot be in class on a specific day for any reason, then I may be able to choose a different day to run presentations (so that your absence will not affect your grade directly).

Audience participation During a presentation, you will be asked to be present and engaged. When you do not understand part of the presenter’s explanation, you must let the presenter know and ask them to clarify. See the previous paragraph for a note on absence.

Overleaf writeup. You will be assigned a written work every non-exam week (most will be done individually and the more challenging ones will be done in groups). The first draft is due on Wednesday at 10am, and the final draft is due on Monday the following week.

You are free to discuss your work with me, other students in the class, and others (be sure to credit your resources). Unless I tell you otherwise, you will schedule a meeting with me on Wednesday or Thursday outside of class to revise your submission. You may request a second feedback (and third) after this meeting.

An Overleaf writeup that is not successful will not be counted towards your grade. However, a written work can be resubmitted past the deadline at the cost of one token.

Weekly quizzes. You will be given a list of definitions, theorems, and exercises (which answers have been discussed in class or are in the back of the section/book). You will need to be able to state definitions and theorems properly. You will also be asked to recognize and provide examples of situations where a definition or theorem does or does not apply. You may re-take or make up two quizzes in my office during the semester (no token needed).

In-class Exams. In-class exams will assess your mastery of definitions, statements of theorems, and proofs from the textbook or lectures. In addition to questions asked of you during the quizzes, you will be asked to construct proofs of theorems which you have seen before. Because you have seen the list of all possible questions, the grading standard for these are higher than on the take-home exams. You are welcome to ask for feedback on your prepared solutions up to the day before the in-class exam day.

You can retake an in-class exam at the cost of a token. Only the most recent outcome will be counted toward your grade. Different questions (from the same list) will be chosen for your second attempt.

Take-home Exams. Take-home exams will assess you ability to write new proofs on your own. You may not discuss the take-home exam with anyone other than me. During the exam, you may not look at resources other than your textbook and notes. You may ask me to look over your exam before submitting it, but I may not answer your questions directly.

Because take-home exams are more challenging than your other tasks (that is, you don’t get unlimited attempts or resources), the grading standards will be lower than the Overleaf writeup. Each problem will be graded successful, quasi-successful, or unsuccessful.

Project The project is only required if you wish to earn a B or above. You will pick a section from the textbook (or another real analysis/proof-based calculus resource approved by me) which is not covered this semester. I will post a list of suggested sections, but you can choose a different topic as long as I approve it beforehand.

You will assign the class a short reading assignment which includes highlighting several important definitions and theorems from your chosen section. Then you will give a lecture (30 minutes) on these definitions and theorems. Your leture proposal (consisting of reading assignment and lecture notes typed in LaTeX) must be first approved by me before you can present.

Your proposal first draft is due two weeks before your presentation day, and your final draft is due one week before your presentation day. The presentation day will fall in April or May.

Grading errors If you notice any grading mistake or have grading questions that are specific to your work, please talk to me during office hours. This must be done within a week after you receive your graded work.

Grading rubric

At the end of the semester, I am required to submit to the college a letter grade reflecting your achievement in this class. That grade will be determined on the basis of a set of specifications in these areas: (1) learning activities, (2) Overleaf writeups, (3) in-class activities (4) in-class exams, and (5) take-home exams.

Requirements for an A:

Learning acitivies
- homework: success marks for all but two (2) homework and Moodle Reading Forum replies
- quiz: pass 100% of the weekly quizzes (two retakes are allowed during the semester)
- project: successful project proposal + successful project execution
Overleaf writeups
- successful proofs for 100% of all writeup assignments (unlimited feedback requests and resubmissions allowed prior to the final draft deadline)
In-class activities
- give a sufficient presentation whenever called to, but 2 unprepared or absent days are allowed.
- during a presentation, be present, engaged, and ready to ask questions or give suggestions. Each week, you have to either ask questions or give constructive comments. You are allowed 2 silent days (a day when you are not physically/mentally present counts as a silent day).
In-class exam: pass 90% of in-class exam questions.
Take-home exam: write an average of four (4) successful proofs on each take-home exam.

To earn an A-, satisfy all requirements for an A grade above, except for the following lower standards for exams:

In-class exam: pass 85% of in-class exam questions.
Pass 90% of the weekly quizzes (two retakes are allowed during the semester)
Take-home test: write an average of three (3) successful proofs and one (1) quasi-successful proof on each take-home exam.

To earn a B+, satisfy all requirements for a B and any two of the bullet points from the A- grade requirements.

To earn a B, satisfy all of the following:

At-home acitivies
- Homework: success marks for all but four (4) homework and Moodle Reading Forum replies
- successful project proposal + successful project execution
- Pass 80% of the weekly quizzes (two retakes are allowed during the semester)
Overleaf writeups
- Submit successful proofs for 90% of all Overleaf assignments by the deadline (unlimited feedback requests and resumbissions allowed up until the deadline)
In-class activities
- Give a sufficient presentation whenever called to, but 4 passes and absences are allowed.
- When someone else is presenting, be present, engaged, and ready to ask questions or give suggestions. You are allowed four (4) silent days (a day when you are not physically/mentally present counts as a silent day).
In-class exams: pass 80% in-class exam questions.
Take-home exams: write an average of two (2) successful and two (2) quasi-successful proofs on each exam.

To earn a B-, satisfy any three bullet points for a B grade, and satisfy the C requirements for the remaining two bullet points.

To earn a C+, satisfy all three bullet points for a C and satisfy any two of the bullet points for the B grade.

To earn a C, satisfy all of the following:

At-home acitivies
- Homework: success marks for all but 6 homework and Moodle Reading Forum replies
- Pass 70% of the weekly quizzes (two retakes are allowed during the semester)
Overleaf writeups
- Submit successful proofs for 70% of all Overleaf assignments by the deadline (unlimited feedback requests and resumbissions allowed up until the deadline)
In-class activities
- Give a sufficient presentation whenever called to, but 6 passes and absences are allowed.
- When someone else is presenting, be present, engaged, and ready to ask questions or give suggestions. You are allowed six (6) silent days (a day when you are not physically/mentally present counts as a silent day).
In-class exams: pass 70% in-class exam questions
Take-home exams: write an average of one (1) successful and two (2) quasi-successful proofs on each exam.

To earn a C- in the class, satisfy any three bullet points for a C grade, and satisfy the D+ requirements for the remaining two bullet points.

To earn a D+ in the class, satisfy all of the following:

Pass 50% of the homework/Moodle reading forum/quizzes given before April 21.
Pass 50% of all Overleaf assignments assigned before April 21
Participate in 50% of class activities during the first 11 weeks of the semester
In-class exams: pass 50% of questions on all in-class exams in Feb-April.
Take-home exams: write one (1) quasi-successful proof on one take-home exam.

To earn a D, satisfy all of the D+ requirements above, where each word pass is replaced with show serious effort in.

(I reserve the right to lower the passing requirements for the course)

Mid-semester (temporary) grade reporting

I will report your (temporary) mid-semester grades (by March 29) as follows.

Letter	Minimum requirements
A	pass 90% of in-class exam questions AND write 4 successful proofs on March take-home exam AND pass 100% quizzes, Overleaf writeup, and presentations
B	pass 80% of in-class exam questions AND write 2 successful proofs on March take-home exam AND pass 90% on Overleaf writeup and presentations, and 80% on quizzes.
C	pass 70% of in-class exam questions AND write 1 successful proof on March take-home exam AND pass 70% on Overleaf writeup, quizzes, and presentations.
D	pass 50% of all assignments and activities

Academic honesty and collaboration policy

Any substantive contribution or help to your submitted work by another person or taken from a website or publication should be properly acknowledged in writing (by citing the source). Failure to do so is plagiarism and will necessitate disciplinary action.

Exams. During an exam (including take-home exams), you may not discuss the exam with anyone other than me (the instructor). You may not use sources other than the textbook (for example, you cannot consult other textbooks or the internet.)

Overleaf writeup. As a guideline for collaboration, I encourage students to get together in small groups to discuss problems. The Overleaf writeup you submit should be your own work (except that you may use other people’s LaTeX code). If your writeup was inspired by a class presentation, this should be cited. Internet and other non-textbook resources are allowed on non-exam assignments (with proper citations).

Group assignments. Anything taken from a source outside the group should be properly cited. In addition, all team members must stand behind all reports bearing their names. Do not include someone’s name in a submission if they do not contribute to the work.

Actions that would cause you to be guilty of plagiarism include the following:

Any evidence of collaboration between students or use of internet resources on an exam
Discussing an exam question (while you or someone else is still working on the exam) with someone other than the instructor.
Handing in a proof (partially or fully) done by someone else under your own name.
Reading someone else’s proof (for example, from another textbook or the internet) and submitting it as your own work.

As a student at Gustavus you are expected to uphold the Honor Code and abide by the Academic Honesty Policy. Read about the Academic Honesty Policy.

The first violation will result in no credit for the assignment or exam in question (tokens cannot be used in these situations). The second violation will result in an F in the class. Both times, an honor code violation report will be submitted.

Gustavus Services

Disabilities Services

Gustavus is committed to all students achieving their potential. If you have a short-term or long-term disability or think you have a disability (physical, learning, hearing, vision, psychiatric, etc) which may need a reasonable accommodation, please go to the Center for Academic Resources and Enhancement (CARE), URL: https://gustavus.edu/advising/disability/, Anderson Hall 107 or 507-933-7227, as soon as possible. You can have a confidential discussion of your needs and appropriate plans. Contact our Accessibility Resources Coordinator, Kelly Karstad, kkarstad@gustavus.edu or x7138).

English Language Learners & Multilingual Services

Support is available for those students whose first language is not English, and/or those who self-identify as multilingual. Contact Corey Sandusky (Multi-Lingual Learner Tutor) at csandusk@gustavus.edu or 507-933-7197 for individual tutoring and consulting services. You can also seek help from peer tutors in the Writing Center (gustavus.edu/writingcenter/).

Other academic services

Contact general academic advising Jane Lalim at jlalim@gustavus.edu or 507-933-6124.

Mental Wellbeing

The Gustavus community cares about all students. Strained relationships, increased anxiety, alcohol or drug problems, feeling down, difficulty concentrating, or lack of motivation may affect a student’s academic performance or reduce a student’s ability to participate in daily activities. If you or someone you know expresses such health concerns or experiences a stressful event that can create barriers to learning, Gustavus services are available to assist you. Learn about confidential health services available on campus at gustavus.edu/counseling/ Johnson Studion Union, room 204 from 8-4:45pm Mon-Fri phone 507-933-7027. See also gustavus.edu/deanofstudents/services/.

(Credit: Joshua Bowman, Pepperdine University and Jeff Ford, Gustavus Adolphus College, used with thanks)