Introduction to Mathematical Reasoning

Summer, s.2 2022

 Lectures: M,W,F 9:00--10:50 Peter 102 Office Hour: M,W,F 10:50--12:00 APM 7230 TA information: Alexander Mathers amathersucsd edu TA Office hour: T, Th 10-12 APM 1151 TA information: Alexander Schlesinger afschles ucsd edu TA Office hour: M, Th 1-3 APM 1202

Book
• Peter J. Eccles, An Introduction to Mathematical Reasoning: numbers, sets, and functions. (The main textbook)
• R. B. Maddox, Mathematical Thinking and Writing: A Transition to Abstract Mathematics.
• D. Smith, M. Eggen and R. St. Andre, A Transition to Advanced Mathematics.
• D. Solow, How to Read and Do Proofs.
Schedule

This is a tentative schedule for the course. If necessary, it may change.

Homework

• Homework will be assigned in the assignment section of this page.
• Homework are due on Fridays at 2 pm and should be submitted on the GradeScope.
• Late Homework are not accepted.
• There will be 5 problem sets. Your cumulative homework grade will be based on the best 4 of the 5.
• If your homework is typed and well-written (based on the TA's judgement), its score will be multiplied by 1.1!
• You can work on the problems with your classmates, but you have to write down your own version. Copying from other's solutions is not accepted and is considred cheating.
• A good portion of the exams will be based on the weekly problem sets. So it is extremely important for you to make sure that you understand each one of them.
• Only a couple of problems in each problem set will be chosen by the TAs and get graded.

• Your weighted score is the best of
• Homework 20%+ midterm exam I 20%+ midterm exam II 20%+ Final 40%
• Homework 20%+ The best of midterm exams 20%+ Final 60%
• Your letter grade is determined by your weighted score using the best of the following methods:
•  A+ A A- B+ B B- C+ C C- 97 93 90 87 83 80 77 73 70
•  Based on a curve where the median corresponds to the cut-off B-/C+.
• If you wish to have your homework or quizzes regraded, you must request regarde through Gradescope within the specified window of time. No regrade will be accepted after the deadline.
• Submitting a regrade request without a legitimate explanation may result in the loss of one point on the given problem.
Further information
• There is no make-up exam.
• Keep all of your returned homework and exams. If there is any mistake in the recording of your scores, you will need the original assignment in order for us to make a change.
• No notes, textbooks, calculators and electronic devices are allowed during exams.
• Academic Integrity: 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.
Exams.

• The first exam:
• Time: Friday, Aug 12, 10-10:50
• Location: Classroom
• Topics: All the topics that are discussed in class and relevant chapters of your book till end of strong induction.
• Questions are fairly similar to the homework assignments and the examples discussed in the class. Make sure that you know how to solve anyone of them.
• Practice: You should first study the lecture notes, then go through the homework assignments, after that study examples mentioned in your book, and the relevant problems in your book. You might find these problems useful. Here is an old first-exam, and here is its solution. Here are A and B are another couple of exams.
• Exam:
• The average in this exam was 24.85.
• A quarter of the students scored at least 31.5 points.
• Half of the students scored at least 27 points.
• Three quarter of students scored at least 20 points.
• Congratulations to Junle X., Aaron K., Jennifer L., and Yujia W. who scored at least 35 points. I commend you for your hard work.
• Unfortunately, there are 12 students who scored below 18 points. This is extremely alarming. You should attend all the lectures, discussion sessions, and take advantage of all the office hours, and available resources in order to improve your understanding of the subject and subsequently your performance in this class.
• The second exam:
• Time: Friday, Aug 26, 10-10:50.
• Location: Classroom.
• Topics: All the topics that are discussed in class and relevant chapters of your book till end of bijection and invertibility.
• Questions are fairly similar to the homework assignments and the examples discussed in the class. Make sure that you know how to solve anyone of them.
• Extra help:
• You may find this practice sheet helpful. Here is a past exam, and Here is its solution. Here is another exam.
• Exam:
• The final exam:
• Date: Saturday, Sep 3, 8-11
• Location: Peter 103
• Topics: All the topics that were discussed in class, your homework assignments, and relevant examples and exercises in the practice exercises and your book.
• Questions are fairly similar to the homework assignments and the examples discussed in the class. Make sure that you know how to solve anyone of them.
• Extra help:
• You may find this set of practice problems useful. I admit that some of these problems are hard, but nevertheless they are good for your practice.
• You may find the posted extra problem set and the main ideas of its solution useful.
Assignments.

Problem sets will be posted here. Make sure to refresh your borwser.

• Due Aug 5: You can find your first problem set here A. Here is the solution.
• Due Aug 12: You can find your second problem set in the following files A and B (From the B file, you should solve Problems 1 and 2; but you should also know how to solve the rest of the problems for the exam). Here is the solution for file A.
• Due Aug 19: You can find your third problem set in the following files: A only problem 4, B, and C (From file C, only problems 1 and 2, for this week). Here is the solution for file A, and Here is the solution for file B.
• Due Aug 26: You can find your fourth problem set in the following files: A (starting from problem 3 from file A), B, and C (from file C, only problem 1). Here is the solution for file A, and Here is the solution for file B.
• Due Sep 2: You can find your fifth problem set in the following files: A (starting from problem 2 from file A), B. Here is the solution for file A, and Here is the solution for file B.
• Extra problems: For your own practice: Here is an extra problem set with outline of solutions.
My notes.

I will post my notes here. You are supposed to read these notes and the relevant chapters of your book.

You might find my notes from Fall 2015 and Fall 2016 useful: Here and Here are links to the webpages of those classes.

• Lecture 1: Here is the lecture note.
• Lecture 2: Here is the lecture note.
• Lecture 3: Here is the lecture note.
• Lecture 4: Here is the lecture note.
• Lecture 5: Here is the lecture note.
• Lecture 6: Here is the lecture note.
• Lecture 7: Here is the lecture note.
• Lecture 8: Here is the lecture note.
• Lecture 9: Here is the lecture note.
• Lecture 10: Here is the lecture note.
• Lecture 11: Here is the lecture note.
• Lecture 12: Here is the lecture note.
• Lecture 13: Here is the lecture note.
• Lecture 14: Here is the lecture note.
• Lecture 15: Here is the lecture note.