| Math 111, Spring 2008 Syllabus |
| Instructor: Dr. Katherine Kelm |
| Office: PB 346 |
| E-mail: Click here |
| Phone: 278-4633 |
| Course: Math 111 (transition to advanced mathematics), class number 42405 |
| Class meets: MWF 9:00-9:50am in S2 308 |
Text:
- Chartrand et al., Mathematical Proofs: A Transition to Advanced Mathematics (ISBN 0201-71090-0)
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| Welcome to Math 111! Math 111 is a 3-unit course, designed to help students make the transition from the "plug and chug" of lower-division mathematics to the theoretical, proof-driven mathematics of advanced courses. Students must pass Math 76 with a C or better in order to enroll in this course. The course covers parts of chapters 1 through 9 of the text. |
| Learning to write rigorous proofs in the language of mathematics can be difficult to master. Please be patient with yourself and with me as you learn this paramount skill. You will be expected to put in a lot of time and effort to learn the material. I will do my very best to teach it to you, but you must ultimately take the responsibility to stay caught up, seek extra help when you need it, and monitor your progress in the class. I am always here to help you do this. |
| I love this course. I hope my enthusiasm rubs off on you! |
| Please see the following links for complete information: |
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| Learning Objectives |
Upon completion of this course, students should understand:
- Importance of a formal, rigorous proof
- When it is sufficient to give an example/counterexample and when an arbitrary element of a set must be considered
- Set operations (intersection, union, difference, complement) and their properties
- Meaning of logical operations (and, or, negation, implication) and quantifiers (universality and existence)
- Difference between different types of proof (direct, by contrapositive, by contradiction, by example/counterexample, etc.)
- Divisibility properties of integer numbers; congruences; basic properties of rational and irrational numbers
- The notions of a relation, equivalence relation; properties of equivalence classes
- The notions and properties of one-to-one, onto, bijective, inverse functions
- Principle of Mathematical Induction
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| Learning Outcomes |
Upon completion of this course, students should be able to:
- Recognize simple statements that can be proved using one of the following techniques, and prove them:
- direct proof
- proof by contrapositive
- proof by contradiction
- vacuous proof
- trivial proof
- proof by cases
- proof by example/counterexample
- proof by induction
- Determine the truth values of simple statements.
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| [ Index | Skip to end ] |
| Course Outline |
| Chapter |
Description |
| 1 |
Sets:
1.1 (describing a set)
1.2 (special sets)
1.3 (subsets)
1.4 (set operations)
1.5 (indexed collections of sets)
1.6 (partitions of sets)
1.7 (Cartesian products of sets)
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| 2 |
Logic:
2.1-2.3 (statements)
2.4-2.6 (implications)
2.7-2.9 (logical equivalence)
2.10 (characterizations of statements)
2.11 (quantified statements and their negations)
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3
4 |
Direct Proof and Proof by Contrapositive:
3.1-3.4 (proof basics)
3.5 (proof evaluations)
4.1 (proofs involving divisibility of integers)
4.2 (proofs involving congruence of integers)
4.3 (proofs involving real numbers)
4.4 (proofs involving sets)
4.5 (fundamental properties of set operations)
4.6 (proofs involving Cartesian products of sets)
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| 5 |
Proof by Contradiction:
5.1-5.5 (proof by contradiction and examples)
5.6 (a review of direct proof, proof by contrapositive and proof by contradiction)
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| 6 |
Prove or Disprove:
6.1 (conjectures in mathematics)
6.2 (a review of quantifiers)
6.3 (existence proofs)
6.4 (a review of negations of quantified statements)
6.5 (counterexamples)
6.6 (disproving statements)
6.7 (testing statements)
6.8 (a quiz of "prove or disprove" problems)
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| 7 |
Equivalence Relations:
7.1 (relations)
7.2 (reflexive, symmetric, and transitive relations)
7.3 (equivalence relations)
7.4 (properties of equivalence classes)
7.5 (congruence modulo n)
7.6 (the integers modulo n)
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| 8 |
Functions:
8.1 (definition)
8.2 (the set of all functions from A to B)
8.3, 8.4 (one-to-one and onto functions)
8.5 (composition of functions)
8.6 (inverse functions)
8.7 (permutations)
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| 9 |
Mathematical Induction:
9.2 (the principle of mathematical induction)
9.3-9.6 (examples)
9.7 (proof by minimum counterexample)
9.8 (the strong form of mathematical induction)
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| You can get an idea of the approximate week we will be studying each topic by looking at the due dates on the Homework List. |
[ Index | Skip to end ] |
| Homework Policy*
Homework is due on Fridays at 11:30am. You may give it to me directly or place it in the slot outside my office labeled with "Math 111". Please turn your paper in the direction indicated above the slot, so all papers will be facing the same way. Please write your full name, the due date, and Math 111 at the top of the first page. Homework will be accepted up to 72 hours late (through Monday at 11:30am) for half credit. After that it will not be accepted. I will drop your lowest homework score. Be sure to read and understand the Homework Format Requirements and Guidelines. They will be enforced! Homework of more than one page must be stapled. This is not optional. Do not write teeny-tiny to get out of this, please!
There is no homework due on midterm exam days.
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| There may be bonus problems (for extra credit) assigned in class from time to time which do not appear on the syllabus. |
| Warning: The amount of homework for this class is substantial. You are expected to budget at least 6-9 hours per week for homework and study outside of class. Do not attempt to concentrate all this work on Thursday nights! You will never finish assignments, let alone learn anything, if you do not start a few days early, while you have the chance to get help. |
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| In-Class Presentations* |
One of the most important and effective ways to learn to prove things is to explain it to someone. Consequently, you will be required to present at least one proof to the class during the semester. A presentation includes the following components:
- A well-prepared explanation of what is to be proved and how you proved it
- Legible visuals for the class to follow
- Answering questions from me or from your peers to the best of your ability
- A neatly written or typed proof to hand in, separate from your regular homework assignment
- Revisions and a re-do of your presentation and written solution, if necessary
In order to help make this process as fear-free as possible, I will assign you to a small group, which will be given exercises to prove and a time slot in class for the presentation. The group will prepare the proof and choose a presenter. The presenter will hand in a polished written solution in his or her own words. I realize it is difficult to go first, so extra credit will be given if you are the first person in your group to present. Everyone in the group must present before someone goes again. The rest of the class is expected to provide constructive feedback and discussion.
More details will be given in class. I reserve the right to reorganize groups if necessary.
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| Midterms* |
| The midterm exams will be Fridays, February 15, March 28, and May 2 (weeks 5, 10, and 15). The sections that will be covered on each midterm will be based on the homework due since the last exam and will be confirmed by announcements made in class. Makeups will be solely at my discretion. You are not eligible for makeup consideration for any reason unless you contact me PRIOR to the start time of the exam. There will be no exceptions to this policy. If you have missed an exam, or feel that you are likely to miss an exam, contact me immediately to discuss your plans for passing the course. |
| IMPORTANT. Reading comprehension is as important in mathematics as in any other subject. On any exam you should expect to see problems which are not exactly like the homework. |
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| Final Exam*
The final exam is comprehensive. It will be held in our regular classroom. Please check the class schedule for the correct day and time for your section. If you feel you might have a conflict, contact me immediately. Please note that it is strictly against University policy for me to give final exams early for any reason. |
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| Attendance |
| Missing class is the single most preventable cause of bad grades! With your group depending on you (see In-Class Presentations, above), it is especially important to make the commitment to attend class every single day, for the entire time period. I will not be able to slow down for you, because that material is going to be needed in all upper-division mathematics courses in the major (and throughout your life), whether we cover it or not. So you simply must show up every day, on time, to avoid missing something critical. |
| There are no excuses accepted for non-attendance. Arriving late and/or leaving early is considered non-attendance. If you are absent on a day your group is scheduled to present, you will receive half credit for your work on the proof. Additionally, if you are the scheduled presenter, you will be required to make up the presentation.
If you feel you will be missing a significant number of classes, please come see me to discuss your plans for passing the course. |
| If you must miss class, get the notes from someone as soon as possible, go over them (preferably with the student who took the notes -- it will be valuable for him or her as well to talk through the material), and then come to office hours with any questions. I cannot repeat my lecture for students who skip class. |
| If you are enrolled and decide not to take the class, you have until Tuesday, January 29 to drop the class without a Serious and Compelling Reason (please see p. 59 of the current course catalogue for details). Please drop as soon as you have made your decision in order to allow others to join the class. |
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| Basis for course grade (What does this mean?) |
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| Homework |
19% |
I drop the lowest of these six grades,
for a total of 19 x 5 = 95% of your grade |
| Presentations/Class Participation |
19% |
| Midterm 1 |
19% |
| Midterm 2 |
19% |
| Midterm 3 |
19% |
| Final exam |
19% |
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| Grade breakdown** |
| 90-100% |
A |
| 80-89.9% |
B |
| 70-79.9% |
C |
| 60-69.9% |
D |
| 0-59.9% |
F |
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| ** Due to possible curving, your grade may end up higher, but not lower, than this chart indicates. |
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Other Stuff
- Calculator Policy
You may use any calculator you wish for homework. However, I recommend that you practice mental math whenever possible, as calculators are generally not allowed on exams. The good news is that the types of problems encountered in this course do not benefit from use of a calculator anyway!
- Classroom Behavior
I wish to maintain a positive, comfortable learning environment in our class. Please show respect for others by:
- Making sure that all cell phones and pagers are turned off for the duration of the class
- Not using tobacco products of any kind in class (this is California law and includes smokeless tobacco)
- Not speaking, whispering, or engaging in any other distracting behavior while someone is addressing the class.
Failure to adhere to these ground rules may result in your dismissal from the class.
- Academic Honesty
Cheating is quite prevalent at Fresno State, and thus the penalties for getting caught are severe. Don't do it. Notes of any kind are not permitted during exams. I may ask for hats to be removed or for you to switch seats for extra security. Collaboration on homework assignments and presentations is allowed and encouraged; however, everyone must turn in his or her own work, in his or her own words. The University policy on academic dishonesty will be followed in cases of cheating and plagiarism. This means, at minimum, a score of 0 on any assignment or exam in which cheating or plagiarism is suspected. Please don't do anything that looks even remotely like cheating. It's not worth it.
In addition, I will be checking your student ID in the last weeks of the term. I will examine your photo, write down the ID number on the back, and compare it with my records. The purpose of this procedure is to help prevent students from hiring impostors to take classes for them. Your grade for this course will not be processed until I have verified your ID. The only exception will be if you earn an F for the course. Thank you for your cooperation.
- Students with Disabilities
The University policy on students with disabilities will be followed. If you have a disability documented with Services for Students with Disabilities which requires accommodation, please see me as soon as possible to make arrangements.
- Computer Use
The University policy on computer use will be followed. You are expected to have access to a computer with which to check email regularly, visit the course web site, and download course materials.
- Extra Help
Do not allow yourself to remain lost in the class. The night before the midterm is not the time to discover that you are in over your head! Whenever you need help, you must get it right away. Sources of help include the following:
- First and foremost, I am always here to help. If you cannot come to my office hours, make an appointment, or call or send email. I want you to succeed! Bringing your concerns to me can only raise your grade.
- Other students. Please share your contact information with your assigned group, and stay in touch with them. Studying with your peers is one of the most effective learning tools and can be a great stress-buster, too. Even if you believe you work best alone, make sure you have someone to contact in case I am not available.
- Supplemental reading materials. There are many good proof-writing books (and online information) besides our text. Please see me for more ideas, or consult a search engine such as Google.
- Bonus Points
There are two ways to get bonus points in this class:
- Do an extra presentation (after everyone in your group has presented).
- In an effort to get to know each of you personally, and to encourage you to find my office, I will give 5 points bonus homework credit to everyone who comes to one or more of my office hours the first two weeks of classes (January 15-25). You do not need to have questions or stay the full hour. Just come and introduce yourself!
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Disclaimer: Although I have no plans to do so, all dates and policies are subject to change or exception according to announcements made in class. |
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| Last updated 1/16/2008 |