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Course:  Math 109   (Course Catalog)

Title:  Mathematical Reasoning

Credit Hours:  4

Prerequisites:  Math 18 or Math 20F or Math 31AH, and Math 20C. (or equivalent)

Catalog Description:  This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilon-delta proofs. Required of all departmental majors.

Textbook:  Book of Proof  (2nd Edition), by Richard Hammack.

Material Covered:  We will cover all of the textbook except Chapter 3. You can find the sections of the book we will be discussing (listed by day we will be discussing them) on the course calendar.

Readings:  It is expected that you read the assigned material in advance of the class period indicated by the course calendar. The amount of reading is not large in quantity; however, it is heavy in conceptual content. You will be expected to write proofs of theorems using the ideas presented in the assigned reading; therefore, it is absolutely vital that you read the assigned material carefully. Moreover, since class periods will center on discussion of problems related to the assigned reading, it is critical that you read the assigned material in advance of the class period it will be discussed

Homework:  Homework will be assigned on the course homework page and should be completed by the indicated due date. You will be asked to turn in written solutions to a subset of the exercises. These homework assignments will be graded carefully and will comprise a substantial portion of your grade: you will be expected to take them seriously and to write them up neatly. A detailed list of homework guidelines may be found on the homework page. Please make every effort to complete all the assigned exercises, not just those you turn in: the assigned exercises will be used as a resource for constructing your exams. Your homework grade will be based on seven (7) assignments. Note that three (3) of the seven (7) assignments are revisions of a previous assignment.

Lectures:  "Lecture" is not really the appropriate term for how the class meetings will be run: instead of formal lectures, class periods will be used for class discussion based on problems given the previous day. These "problems to think about" will be chosen to illustrate the important concepts addressed in the assigned reading for that class period. You will be expected to actively participate in class discussions by (1) asking questions and (2) making suggestions for solving the problems. By actively participating, you will gain the deeper understanding required to analyze mathematical statements and construct your own proofs.

iClickers:  In order to facilitate discussion of conceptual ideas, we will be using the iClicker classroom response system. To register your clicker via TritonEd, follow the i>clicker Remote Registration link from the Tools page. For iClicker questions, you will be graded on participation. If a student participates in 80% of iClicker questions on a given day, that student will get full credit for that day.

In-Class Work:  Much of our in-class time will be spent working on exercises. These will be done in groups and will be presented to the class by students. At the end of the class, each group will turn in their work, which will be graded on completion. Every student must present at least one exercise in class.

Electronic Computing Devices:   Graphing calculators and computer programs (or online computing websites such as Wolfram|Alpha) can be very helpful when working through your homework. However, a calculator/computer should be used as an aid in the learning concepts, not just as a means of computation. You should use these devices when working on math problems at home, but always keep in mind that you will not be allowed access to any electronic computing devices during exams or quizzes. Of course, this also means that you will not be asked to solve problems on exams or quizzes that require the aid of an electronic computing device.

Exams:  There will be one final exam. Check the  Course Calendar  for the exact dates of the final exam. You may use one 8.5 x 11 inch page of handwritten notes. (Both sides are okay, but no photocopies are allowed.) You may not use any other notes or any electronic devices. Please bring your student ID to the exams.

  • You may bring ONE 8.5 x 11 inch sheet of handwritten notes. You may use both sides. (No photocopies!)
  • No books may be used during the examinations.
  • No calculators will be allowed during the examinations.

It is your responsibility to ensure that you do not have a schedule conflict involving the final examination. You should not enroll in this class if you cannot sit for the final examination at its scheduled time. You must pass the final exam ( >59% ) in order to pass the class. (The actual required percentage may be lowered, depending on overall class performance.)

Grading:  Your course grade will be based on the following formula:

  • 40% Homework,   10% In-class Work,   10% iClicker,   40% Final Exam
After your weighted average is calculated, letter grades will be assigned based on the standard grading scale:

A+ A A- B+ B B- C+ C C- D F
[99,100] [93,99) [90,93) [87,90) [83,87) [80,83) [77,80) [73,77) [70,73) [60,70) [0,60)

We may adjust the scale to be more lenient, but we guarantee that the grade corresponding to a given percentage will not be lower than specified by the above scale.  There will be no curve, but we may adjust the scale to be more lenient (depending on the performance of the class).

Please notice that outside factors, including the need for a certain grade for admission/retention in any academic program, scholarship or transfer credit, graduation requirements or personal desire for a specific grade DO NOT appear in the above calculations, and thus are not considered in any way in the determination of your course grade. Effort, improvement, class attendance and participation will all dramatically improve your grade in the course in that they will allow you to do well on quizzes, exams, and the final exam. They will NOT, however, actively participate in the calculation of your course grade.

Gradescope: Grading will be done using an online tool called Gradescope (

Exam Grading: Exams will be scanned and uploaded to Gradescope and will be graded within it. As a consequence, exams will not be returned to the students. Instead, a digital version of your exams will be made available after the grading has been completed. An email will be sent from Gradescope when the exams are made available.

Regrades:  Regrade requests will be made using the built-in regrade request feature in Gradescope. There will be a limited window of time after the exams are made available during which the regrade request feature will be active. This time window will be announced when the exam scores are released to the students.

Academic Dishonesty:  Academic dishonesty is considered a serious offense at UCSD.  Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.  It is in your best interest to maintain your academic integrity. (Click here for more information.)

Suggestions:  Below are some suggestions that I hope will help you to succeed in this course:

  • Spend sufficient time on the course. According to the policy of UCSD's Academic Senate, "The value of a course in units ... shall be reckoned at the rate of one unit for three hours' work per week per quarter on the part of the student." During a ten-week quarter, for a 4 credit course, you should be willing to spend about 12 hours per week on the course. (So for a 4 credit course during a five-week Summer Session, you should be willing to spend 24 hours per week on the course.)
  • Keep up with the homework and do not miss a midterm. Missing a homework assignment will hurt your grade because no homework scores will be dropped. This policy is designed to encourage students to complete all the assignments and reward those who do.
  • Get started on the homework assignments early. This will enable you to make the most of your discussion section time by coming prepared with specific questions.