Math 111. Transition to Advanced Mathematics. Fall 2021.

Prerequisite: Math 76 (Calculus II).

Hours: 4.

Catalog description: Introduction to the language and problems of mathematics. Use of LaTeX as a typesetting tool. Topics include set theory, symbolic logic, types of proofs, and mathematical induction. Emphasis on students constructing, explaining, and justifying mathematical arguments through active learning.

Course goals
Upon completion of this course, students should know/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

Learning outcomes
Upon completion of this course, students will be able to do:

• Recognize simple statements that can be proved using one of the following techniques, and prove them:
• direct proof
• proof by contrapositive
• vacuous proof
• trivial proof
• proof by cases
• proof by example/counterexample
• proob by Induction
• Determine the truth values of simple statements.
• Type mathematical texts in LaTeX.

 Homework 100 points Test 1 50 points Test 2 50 points Test 3 50 points Final exam 150 points Total 400 points

 Points earned Grade 360-400 A 320-359 B 280-319 C 240-279 D 0-239 F

Class attendance is strongly encouraged and expected. In addition to new material, important course information such as homework assignments will be given, homework may be discussed, and sometimes handouts may be distributed in class.

Exams: There will be three tests (50 minutes long each) and one final comprehensive exam (2 hours long). If for any reason you can not take a test at the scheduled time, please let me know as soon as possible, and certainly before the test. See schedule for exam dates.

There will be a few extra credit opportunities. To be eligible for extra credit, you must have your camera turned on every class.

Extra Help: It is essential not to fall behind, because most classes will use the material studied previously. If you have trouble with some material, seek help in the following ways:

• Ask me, either in class or privately. Don't be shy to ask questions. If you don't understand something, chances are very high that somebody else doesn't understand that either. So your classmates will be thankful to you for asking questions in class! My contact info is given on the course web page. Questions about homework are welcome as well. However, after you got help from me, you should put aside all the notes you made while talking to me, and write a complete solution from scratch, in your own words. I rarely write complete sentences during my office hours, I may only help you to find an approach, an idea. You are responsible for writing a complete solution. Just copying formulas and pictures from my white board and notes will receive zero credit.
• Work with your classmates. Note: working on your homework together is encouraged, however, every group should write down their solutions on their own. If somebody is helping you with your homework then the same rules as for my helping you apply, i.e. you should put aside all the notes and write a complete solution from scratch, in your own words. That way you will learn the best.
• Do also problems that were not assigned. Use the answers and hints in the back of the book to check your answers.
If you are having any difficulties, seek help immediately - don't wait until it is too late to recover from falling behind, or failing to understand a concept!

Students with disabilities: upon identifying themselves to the University, students with disabilities will receive necessary accommodation for learning and evaluation. For more information, see http://www.fresnostate.edu/studentaffairs/ssd/

Academic honesty: cheating and plagiarism will not be tolerated in this class. For information on the University's policy, see the University Catalog (section Policies and Regulations).

Honor Code: Members of the CSU Fresno academic community adhere to principles of academic integrity and mutual respect while engaged in university work and related activities. You should:

• understand or seek clarification about expectations for academic integrity in this course (including no cheating, plagiarism and inappropriate collaboration)
• neither give nor receive unauthorized aid on examinations or other course work that is used by the instructor as the basis of grading.
• take responsibility to monitor academic dishonesty in any form and to report it to the instructor or other appropriate official for action.

Computers: At California State University, Fresno, computers and communications links to remote resources are recognized as being integral to the education and research experience. Every student is required to have his/her own computer or have other personal access to a workstation (including a modem and a printer) with all the recommended software. The minimum and recommended standards for the workstations and software, which may vary by academic major, are updated periodically and are available from Information Technology Services or the University Bookstore. In the curriculum and class assignments, students are presumed to have 24-hour access to a computer workstation and the necessary communication links to the University's information resources.

Disruptive Classroom Behavior: student conduct which disrupts the learning process will not be tolerated and may lead to disciplinary action and/or removal from class.

Subject to Change: This syllabus and schedule are subject to change in the event of extenuating circumstances. If you are absent from class, it is your responsibility to check on announcements made while you were absent.