Mathematicians, computer scientists, and statisticians have to think abstractly, reason logically, formulate ideas precisely, solve problems effectively, and communicate clearly their results to others through the writing of convincing proofs. In this course, you will learn some of these essential skills. Additionally, you will learn some of the fundamental concepts in logic, graph theory, combinatorics, and analysis.
Student Learning Outcomes
- Students should be able to read and understand formal(mathematical) proofs of various types.
- Students should be able to construct, write and explain their own proofs in set theory, combinatorics, graph theory, and introductory analysis,
- Students will develop problem-solving techniques.
Student Learning Outcomes for WritD credit
- Students choose effective rhetorical strategies shaped by their appreciation for the purpose, audience, and context for the writing task.
- Students use writing as a tool to explore ideas, assimilate new knowledge, and reflect on the purpose of their learning.
- Students use writing to evaluate texts critically, and to create arguments that communicate effectively with varied audiences, while acknowledging the limits of their own judgments.
- By using writing to explore ideas, writing multiple drafts, responding to peer and faculty comments, using the Writing Center, revising and polishing written work, students develop flexible tools for effective communication, including a self-critical approach to their work.
- Students create written works that exemplify the structures, genres, and conventions within the discipline.
Mathematical Thinking Problem-Solving and Proofs, Second Edition, by John D'Angelo and Douglas West. Reading assignments for each day of class are posted on the Moodle page for this course. Note that each assignment lists the pages you are supposed to read and gives you problems to do to check your understanding. To help you prepare for class, you will complete a reading reflection sheet to turn in before each class.
Classes will be used for lectures, problem solving, discussions, and other fun activities. Classes, reading assignments, and homework are designed to help you learn. In this course, you are both capable of and expected to learn some of the material on your own; not every topic in the reading or homework will be covered in class. Attendance, both physical and mental, is required. Should you need to miss a class for any reason, you are still responsible for the material covered in that class. This means that you will need to make sure that you understand the reading for that day, that you should ask a friend for the notes from that day, and make sure that you understand what was covered. If there is an assignment due that day, you should be sure to have a friend hand it in or put it in my departmental mailbox (in Olin 312). You do not need to tell me why you missed a class unless there is a compelling reason for me to know. If you have a serious emergency that means you will need to miss an exam, you should be sure to notify me by 8:00 am of the day of the exam.
Weekly homework assignments are listed on the course Moodle page. Every Monday, I will collect the previous week's problems and provide you with feedback on your work using these guidelines. You are encouraged to rewrite and resubmit the problems the following week. As this work is intended to give you practice in preparing for tests, it will not be graded. However, some of your re-written proofs will become part of your course portfolio.
You are welcome to discuss the problems with your classmates but each of you should write up the solutions by yourself. If you do talk with other classmates, you should acknowledge this in your written work. Looking for (and using) solutions over the internet is not allowed as it will not help you learn and understand the material. Using sources other than your textbook, your classmates, and me will be considered cheating.
You will be asked to assemble a portfolio where you reflect on what you've learned about writing and problem-solving. This portfolio will contain samples of writing from the homework, samples of peer-reviews that you've done for other students, and short writing assignments. I will collect portfolios about every three weeks.
There will be three tests: two in-term exams and a final exam. The in-term exams will most likely be closed notes and closed book limited-time (2 hours) take-home tests that you check out and then check in when the time is up. They are tentatively scheduled to be given on Monday, October 14 and Moday, November 11. The final will be a two hour exam that covers the material we learned after the second exam. It is scheduled for Monday, Dec. 16, from 3:30 -5:30 pm.
Your grade is a measure of your learning and growth in the course, rather than a set of points to be “earned” or “lost.” Viewed this way, a grade shows the extent to which you have mastered and can communicate important concepts and ideas. Not all work is graded – you do many things in a course that contribute to your learning: reading, writing, revising, thinking, talking, and listening. It is useful to think of work, then, as the set of activities that contribute to learning. Graded work is that subset of activities where you show how well you have learned to reason mathematically and how well you can communicate your reasoning to others. The graded course components will contribute to your grade in the following proportion:
|In-term exams||29% each|
Letter grades are assigned using the following table.
|A 93-100||A- 90-92.9||mastery of the material with developed insight|
|B+ 87 -89.9||B 83-86.9||B- 80 -82.9||mastery with limited insight|
|C+ 77-79.9||C 73 -76.9||C- 70-72.9||basic knowledge with limited mastery|
|D+ 67-69.9||D 60- 66.9||F 0-59.9||minimal to unacceptable performance|
You are expected to to adhere to the highest standards of academic honesty, to uphold the Gustavus Honor Code and to abide by the Academic Honesty Policy. A copy of the honor code can be found in the Academic Bulletin and a copy of the academic honesty policy can be found in the Academic Polices section of the Gustavus Guide. On the homework problems, I encourage you to discuss problems and their solutions with each other. However, each of you should first make a real effort to solve each problem by yourself. Furthermore, each of you should write up the solutions individually. Note that you may not consult sources other than the text, your classmates, and me. On exams, you are expected to work completely by yourself and use only the allowed sources. You will be expected to sign the honor pledge on homework and exams. The first violation of this policy will result in a 0 on that assignment and notification of the Dean of Faculty. Further violations will result in failing the course.
Gustavus Adolphus College is committed to ensuring the full participation of all students in its programs. If you have a documented disability (or you think you may have a disability of any nature) and, as a result, need reasonable academic accommodation to participate in class, take tests or benefit from the College's services, then you should speak with the Disability Services Coordinator, for a confidential discussion of your needs and appropriate plans. Course requirements cannot be waived, but reasonable accommodations may be provided based on disability documentation and course outcomes. Accommodations cannot be made retroactively; therefore, to maximize your academic success at Gustavus, please contact Disability Services as early as possible. Disability Services is located in the Advising and Counseling Center. Disability Services Coordinator Laurie Bickett (x6286) can provide further information.
Help for Students Whose First Language is not English
Support for English Language Learners and Multilingual students is available through the Academic Support Center and the Multilingual/English Language Learner Academic Support Specialist, Laura Lindell (x7197). She can meet individually with students for tutoring in writing, consulting about academic tasks and helping students connect with the College’s support systems. When requested, she can consult with faculty regarding effective classroom strategies for ELL and multilingual students. Laura can provide students with a letter to a professor that explains and supports appropriate academic arrangements (e.g. additional time on tests, additional revisions for papers). Professors make decisions based on those recommendations at their own discretion. In addition, ELL and multilingual students can seek help from peer tutors in the Writing Center.
Help for any student who is struggling
Your ability to succeed in this course is not predetermined. If you do not think you’re learning as much as you should be, or if your class performance doesn’t reflect the work you’re putting into the course, please come to see me in my office. We will work together to identify ways that you can learn more effectively.