Math 287, Fall 2021 Syllabus

1. Course Information
   1. Instructor
   2. Section
2. What this course is
3. Course Learning Outcomes
4. Required Textbook
5. Grading
   1. Components of course grade
   2. Class activities
   3. Homework
      1. Turning in written assignments
      2. LaTeX
      3. Homework format
   4. Midterm exam
   5. Final exam
6. Preparation and participation
   1. Preparation
   2. Participation
   3. Grade
7. Help
   1. Student times
   2. Mathematics Department Tutoring
   3. University Resources
   4. Additional Help
8. Important Dates
9. Other

Course Information

Course Number:

Math 287

Course Title:

Mathematical Proofs & Methods

Catalog Statement:

An introduction to formal mathematical language, mathematical experimentation, mathematical proofs, mathematical communication, and technologies supporting the above. Core content includes sets and functions, elementary number theory and induction, and distances and topology on the real line. Additional content drawn from logic, combinatorics and probability, graph theory, and modular arithmetic.

Prerequisites:

MATH 175 and MATH 189

Instructor

Instructor:

Zach Teitler [he/him/his]

Email:

zteitler@boisestate.edu

Website:

https://zteitler.github.io

Office:

MB 233A

Office Phone:

208-426-1086

Section

Section Number:

001

Meeting Times:

MoWe 12:00PM - 1:15PM

Meeting Remotely:

We will meet remotely using Zoom. Zoom sessions may be recorded for students who are not able to attend.

Zoom meeting ID:

TBA

What this course is

Higher mathematics requires a significantly different way of thinking. There is a much greater focus on the truth, or falsehood, of statements and connections between facts. There is much less focus on algorithms (methods for doing problems).

Some students think math is merely a list of procedures–a succession of algorithms for “how to do” things. Proof is a major part of mathematics that is not at all like that conception of mathematics. So, you may need to change your attitude about what math really is. It is hard for anyone to change their attitude about anything, so this part may be difficult for you.

This course is an introduction to higher-level, abstract mathematics: the language of mathematics; logic; definitions; topics such as sets, functions, relations, convergence, and series; and especially, proofs. You will get to practice writing formal mathematics (proofs) and you will get feedback on your writing.

This will be a challenging course, and you should expect to spend a lot of time and effort on it; the ultimate responsibility for what you learn is your own. I hope you will find that mathematics is broad, rich, interesting, and useful, and that you can personally be mathematically creative and have a real feeling of accomplishment from it. We should also have fun and stretch our brains at the same time, which is what I think doing mathematics is all about.

Course Learning Outcomes

By the end of this course, students will be able to:

1. Explore mathematical definitions and evaluate mathematical statements.

2. Read and write mathematical proofs at an intermediate level.

3. Demonstrate content knowledge in areas of mathematics including set theory, functions, elementary discrete mathematics, elementary number theory, and elementary continuous mathematics. Recognize connections between these areas.

4. Use technologies to support mathematical exploration and communication.

These learning outcomes will support students in being prepared for upper-division mathematics courses.

Required Textbook

The Art of Proof: Basic Training for Deeper Mathematics by Matthias Beck and Ross Geoghegan, 2010, http://math.sfsu.edu/beck/aop.html

You are required to have this book. You will need to prepare for class by reading sections from the book before class, so that you are ready to learn in class. You will need to have the book available during class, to be able to work on exercises in groups in class.

You can choose what format of the book will be best for you. A PDF version of the book is available from the authors for free (legally!). If you want to, you may also order a printed copy of the published book.

I recommend downloading the free PDF and also buying a printed copy of the book, if you are able to. But it is not required. If you only use the free PDF, that is completely fine.

Grading

Components of course grade

Course grades will include participation in class activities, homework, a midterm exam, and a final exam.

Class activities

A significant amount of class time will be spent working in groups on activities from the course textbook, to practice and learn concepts and skills in the course.

Homework

Homework will consist of weekly assignments. These will be individual written assignments so that you can get feedback on how you are doing in the course.

It will consist mostly of problems from the textbook. Most homework problems will be to write proofs.

You are strongly encouraged to work collaboratively on homework but you must turn in your own solutions.

Turning in written assignments

Homework submissions and grading will be paperless. You will turn in your homework by uploading PDFs to Gradescope.

LaTeX

Part of this class is to learn to “technologies to support mathematical exploration and communication”. The first technology in our list is LaTeX. In our class we’ll learn how to use LaTeX to write math documents. Your homework will be typed in LaTeX.

LaTeX tutorials are available online, e.g., https://www.latex-tutorial.com and https://www.gnu.org/software/teximpatient/. You may wish to use a free online LaTeX system such as https://overleaf.com. (Overleaf includes a LaTeX tutorial.) I strongly recommend Overleaf for students who are new to LaTeX.

Homework format

Use a new page (\newpage) for each problem. State which question you are answering (textbook section and exercise number) and the actual question. Then, start your answer in a new paragraph.

For legibility, use the 12pt option (\documentclass[12pt]{amsart}) and \linespread{2.4}.

Midterm exam

The midterm exam will be an individual written exam in the 8th week of the semester. It will include a component during class time (attendance is required). It may include a take-home component (to be announced).

Final exam

The final exam will be an individual written exam. It will include a component during the scheduled final exam time (attendance is required). It may include a take-home component (to be announced).

Preparation and participation

Preparation

Preparation for class includes reading relevant textbook sections before class, being ready to learn about that topic in class, and knowing what questions you are planning to ask about homework or previous topics.

It’s okay if reading the textbook sections before class isn’t enough to understand the material. The point is to read the section in order to be ready to learn about it in class. Class discussion of the topic should answer many questions and clarify the reading. Following class, please re-read the section to fill in details.

Participation

Constructive participation includes answering or attempting to answer questions in class, asking good questions, and being respectful of others.

In most weeks, our class plan will be:

Monday:

I will present material and answer questions. I will introduce a new chapter and work some of the problems from the chapter, as demonstrations. There may be some class activities (group work).

Wednesday:

I will answer questions. Other than that, the class will be almost entirely activities (group work). Most of the work will be working more problems from the chapter.

There are some exceptions for review and exams, and also where some short chapters are combined into a single week to save time.

Grade

Lack of preparation and participation causes distractions and degrades the course experience for other students in the course. Therefore failure to meet expectations may result in a penalty of up to 10% in your overall course grade (at instructor’s discretion).

Help

Student times

I am here to support your learning. I encourage you to meet with me when you feel that you need support or assistance.

In Fall 2021 I will be available:

Student drop-in hours:

Thursdays 10:30am-12:30pm

Student appointment hour:

Thursdays 12:30pm-1:30pm (email me to set up an appointment within this hour in 15-minute segments)

Additional appointments:

Email me to set up an appointment on other days or times

Student times will be remote via Zoom using my office zoom link (listed in Canvas, or email me for the link).

Mathematics Department Tutoring

Tutoring for Math 287 is available in MB 136 (computer lab in the Mathematics Building). More information will be posted when it is available.

University Resources

Boise State University’s The Basics web page has links to many forms of support, ranging from academic resources to family, living, and food resources.

Boise State University’s Writing Center may be helpful.

Additional Help

You may reach out to me at any time if there’s anything I can help with or if there’s anything you think I should know.

Important Dates

Monday	8/23	First day of classes
Monday	9/3	Last day to register/add or to drop without a W
Monday	9/6	Labor Day. No classes.
Friday	10/29	Last day to drop with a W or completely withdraw
	11/22-28	Thanksgiving Holiday. No classes.
Friday	12/10	Last day of instruction for regular classes
Monday	12/13	Final Exam, 12:00 p.m.-2:00 p.m.
Tuesday	12/21	Grades due. (You will be able to see your grade by this date.)

Other

Respect for Diversity:

Students from all backgrounds and with all perspectives are welcome in this course. It is my intent that all students be well served by this course, that students’s learning needs be addressed both in and out of class, and that the diversity that students bring to this class be viewed as a resource, strength, and benefit. It is my intent to maintain a classroom atmosphere that is welcoming and respectful of diversity: gender, sexuality, disability, age, socioeconomic status, ethnicity, race, and culture. Your suggestions are encouraged and appreciated. Please let me know ways to improve the effectiveness of the course for you personally or for other students or student groups.

ADA Policy Statement:

Students with disabilities needing accommodations to fully participate in this class should contact the EAC. All accommodations must be approved through the EAC prior to being implemented. To learn more about the accommodation process, visit the EAC’s website at https://www.boisestate.edu/eac/new-students/.

Email:

In accordance with Boise State University Policy #2280, it is expected that you will receive and read emails sent to your boisestate.edu email address.

Communication:

Additional information and updates may be announced in class, sent by email, and/or posted on Canvas (https://boisestatecanvas.instructure.com/).

Academic Integrity:

Getting answers to homework or exam problems from unauthorized sources is a very serious form of academic misconduct.

Behavioral Expectations:

Every student has the right to a respectful learning environment. In order to provide this right to all students, students must take individual responsibility to conduct themselves in a mature and appropriate manner and will be held accountable for their behavior in accordance with Boise State University Policy #2050.