## Ams 301 Homework Solutions

## Communicating Mathematics through Homework

Learning mathematics at Harvey Mudd College involves learning how to communicate your ideas effectively. As a student, much of this communication will be in the form of homework. Therefore, so that we may provide you with meaningful and worthwhile feedback, it is important that you put your homework in an easy to read, easy to navigate format. After all, how you present your work should enhance the ideas you are trying to communicate, not impede them.

Suggested Homework Format

With that goal in mind, the following are some suggestions for submitting homework in your mathematics courses:

- Your handwriting should be legible.
- Homework with multiple pages should be stapled in the upper left-hand corner.
- In the upper right-hand corner you should write (in this order)
- Your Name
- Your Class and Section Number
- The Homework Set Number
- The Due Date of the Homework

- Problems should be clearly labeled and numbered on the left side of the page. There should also be a visible separation between problems.
- Each solution should begin with the original problem statement.
- You should leave the top left margin and the entire left margin blank so that graders may use this space for scoring and comments.
- To ensure that each problem is graded, problems should be written in the order they are assigned.
- It is good practice to first work out the solutions to homework problems on scratch paper, and to then neatly write up your solutions. This will help you to turn in a clean finished product.
- Some classes allow you to work jointly on assignments. You should write up your solutions by yourself, unless you are specifically told otherwise by your instructor. Also, you should always acknowledge any help received, at the top of the assignment or in the margin.

## Using LaTeX to Format Your Homework

The department provides a LaTeX class file and supporting templates and instructions that you can use to format your homework. By using the class, you can have all the power of LaTeX for typesetting your mathematical expressions and textual answers as well, with none of the hassles that come with Word, and none of the worries that come with writing your solutions by hand!

The class, templates, and documentation are maintained on GitHub, at

### Just the Document Class and Templates

The following links are to the latest version of the class, available from our GitHub page:

__Grading breakdown:__Homework and Quizzes: 25%, Exams: 20%/25%/30%.

__Exams__

There will be three in-class exams, potentially with take-home components. Of the first two exams, your lower score will be worth 20% of your grade, and your higher score will be worth 25%. The last exam will be somewhat cumulative, and worth 30%. Exams are to be exclusively your own work. In-class exams will be closed to everything, save for one page of notes. Exams are scheduled for **10/4**, **11/8**, **12/11**. No make-up exams will be given except in extreme circumstances.

__Quizzes__

These will be quick 15-20 minute in-class affairs. Closed notes/books/etc.. We will have about four of these in total, coming every couple of weeks, except exam weeks. Quizzes are tentatively scheduled for **9/6**, **9/25**, **10/23**, **11/22**. No make-up quizzes will be given except in extreme circumstances.

__Homework__

Regular homework will be due on Wednesdays in class (unless otherwise specified due to weird scheduling or special assignment format), based on the previous week's material, and will be posted below. See "Writing guide" below for stylistic guidelines and tips on getting started with LaTeX. I prefer solutions typed in LaTeX. If you turn in solutions written by hand, turn in **final draft** quality write-ups—draft up your solutions separately, and then write them up formally.

Research paper summaries (see below for details) are to be handed in at any time, but no later than **11/15** for the first one, and **12/20** (submitted by email) for the second one.

__Academic integrity__

On exams or quizzes, your work must be your own. On homework, however, you are welcome and encouraged to work with each other, and to talk to me and anyone else who knows algebra while solving homework problems. You are also welcome and encouraged to proofread each others homework write-ups. Your write-ups should be your own, though, and final drafts should be written on your own. Additionally, every solution to Dummit & Foote is available online (e.g. project crazy project); I have three things to say on this subject: (1) They're a terrible resource for *starting or getting through* a solution—for the harder problems, these are rarely the best solutions and are occasionally just *wrong*; for easier problems, you are robbing yourself of the essential practice of getting unstuck/asking for help. Homework exercises are only worth 10% of your grade, and the entire point is to get practice. (2) They're a somewhat reasonable resource for a sanity check *after* you've finished a problem—is your argument complete? have you missed anything subtle? what's another solution? etc.. (3) Yes, I'm aware of them; of course, copying these or any other solutions, even with small changes, is considered cheating and plagiarism. So don't do that. Of course, this class is covered by the CUNY Policy on Academic Integrity. See also Richard Neidinger's *Avoiding Plagiarism in Mathematics*.

__Outline of content__

I expect that we will cover the following:

- Ch 0-3, all sections;

Ch 4, sections 1-3;

Ch 5, section 1;

Ch 7, sections 1-4;

Ch 8, all sections.

__Course expectations__

I expect the following from you throughout the semester.

- Before class:
- Skim the listed reading for the week.
- Review your notes from the previous day's class, making notes of any questions you still have.
- Print the day's printable notes and any listed handouts, or bring a device on which you can access them during class.

- In class:
- Come to class! If you have to miss class, spend the extra time reading the book and note outlines; contact a classmate to get the rest of the notes from that day; and contact me if you need to miss more than one day.
- Participate! Ask and answer questions, engage with me and each other, and work actively on in-class exercises.
- Hand in homework every week, on time, and in final draft form.

- After class:
- Now,
*really*read the listed reading. The book is filled with great examples and explanations that we just don't have time to cover in class, and the notes posted here are not complete! - Come to office hours at least once this semester. If you can make the regularly scheduled time, just come. If you can't, make an appointment! To do this, mention to me in class that you'll be sending me a scheduling email. Then follow up with an email requesting an appointment, including your available times, and what you would like to discuss.
- For every hour in class, you should be spending about 3 hours outside on reading, homework, etc.. For this course, that means 10 hours/week.
- Spread out your homework throughout the week, so that you have time to ask questions before it's due. I expect many of the exercises to be challenging, and to take time and work to get through—it's ok if you get stuck! That's the point! Take some time to puzzle on things on your own, and then team up with me or your classmates to chip away at it. Of course, this process takes time, so don't put off starting it. Here's a great article on the importance of getting stuck in mathematics.

- Now,
- In general:
- Communicate! If you're confused, lost, swamped, or whatever, say so. Even if you don't know what questions to ask, let me know you're missing something, and I will try to get you back on track.
- Get to know me and your classmates professionally. Math is best as a collaborative experience, and your classmates are some of your best resources. Talk to each other, work together, explain things and ask questions. If you don't have time to get a study group together on campus, find out who else lives or works near where you do, and make time that way.
- Be honest and work with integrity; if you slip up, come talk to me and we'll work out a fair way to proceed.
- Have fun! Algebra can be challenging, but it's also a
*fun*topic. Learn to play with the ideas: do examples, make hypotheses, and prove results by explaining why things are true with precision and style.

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