There is little doubt that math is useful: it is used throughout the sciences and engineering, from quantum mechanics and weather prediction to space flight to nanotechnology and financial modelling. But that is just part of the story. When you study mathematics, you learn about the language of science. You gain access to the ideas of several of the greatest scientific minds humanity has produced, like Newton, Leibnitz, Euler, Gauss. Whether you believe it or not, as the distinguished mathematician I. Gelfand said, "the most important thing a student can get from the study of Mathematics is the attainment of a higher intellectual level".

The goal of Math 221 is to give the student knowledge of several basic topics (logic, integers, sets, functions), in a set of increased formality with respect to early university math classes. One of the big strengths of math as a science is the possibility of proving results with absolute certainty (within a certain axiomatic framework). This class was designed to give the student a first taste of how things are proven in math.

With Mathematics, like with any advanced skill, the learning process is never quick nor painless. Here are a few things to be considered that might help you succeed in this class:

- This class requires the student to make a step beyond the level of mathematical maturity achieved in Math 110. Many ideas and notions are discussed along the course, and it is almost impossible to memorize them all, and even less to use them effectively. It is all about understanding and practicing. So, practice-practice-practice is the name of the game. The assignments, and even the recommended practice questions, are only the tip of the iceberg. This class requires you to read and practice continuously. The maturity required to succeed in this class cannot be obtained in a mad-rush night-before-the-midterm style.
- Keep up with the material covered in class. Mathematics classes tend to build directly on what you have already learned. If you fall behind it can be very difficult to catch up.
- Do lots of practice problems. If you can barely do the questions from the assignment, it is hard to imagine that you would be able to do a related question, without help, under the stress situation of the exam. Conclusion: practice, practice, practice.
- Take advantage of the additional resources available to you. These include the textbook, the instructor's office hours, additional resources for students, information on the web, etc.
- The topics will become second nature if you take the time to understand why it is what it is, and then use it by doing lots of problems.
- Study with the goal of understanding "why" instead of just trying rote memorization.
- Make sure to present your work clearly, and stapled.

** Practical matters**

**Grading scheme:**20% Assignments, 30% midterms, 50% final.**Prerequisites:**The official prerequisite for this class is Math 110 and one of Math 111, 122, 127 . We will not use many topics from those courses, but rather expect the student to be mature enough to deal with content in a more abstract way. For certain, basic algebra and geometry should be mastered by the student. If you are unsure of what to expect, I will assume that the contents of the following two short chapters are familiar to you:- Basic Algebra (all topics mentioned in this link).
- Basis Analytic Geometry (all topics mentioned in this link).

"Familiar" above means that

**you can do the exercises on your own, and correctly**.**Textbook:**We roughly follow*Introduction to Mathematical Thinking: Algebra and Number Systems*, by Gilbert and Vanstone, 5th edition. There is not absolute need to have the book, but it will definitely be a good resource to read some of the material.-
**Midterms:**the two midterms will take place on February 17th and March 24th. To compensate for emergencies and bad days, if the grade in the final exam is higher than the worst midterm, the grade from the final exam will be used instead of the grade on that midterm. **Final Exam:**the comprehensive three-hour final exam will take place on April 17th, from 9:00 to 12:00. Location to be announced (this will be confirmed closer to the date). Please bring**photo id**to the exams.**Assignments:**Weekly assignments will be published every Friday, due the following Friday at the beginning of class. Group work can help a lot, if it means that the group works together towards building a solution to each problem. "Group work" of the kind "I copy the solution from whoever gets it" might work for the assignments but will not help you for the exams (which comprise most of the class' marks), and it will get you in trouble for plagiarism.**Practice:**You don't learn any mathematics by just listening and watching. You learn mathematics by**doing**, and thinking about it. That's what the assignments are for, but usually you shouldn't consider them enough practice. For this, suggested problems from the book will be indicated in the course web page. You will know you have practiced enough when you can take questions from the suggested list, solve them in a decent amount of time, correctly, without looking at the book nor asking for help. Until this happens, keep practicing, and use the resources you have available to improve.**Communication:**you can reach me by email, either through the course web page or through UR Courses. The links there automatically write "Math 221-001" in the subject, so that I know what the email is about, and my spam filter will let it pass. I will happily answer short concrete questions I get by email. I will not answer emails of the form "please explain me this topic". If you need more detailed help, please come to the office hours, or use one of the several tutoring solutions offered by the university. UR Courses also has a forum feature, feel free to post a question there, or reply to what others post.**Additional resources:**The course web page lists several options to get personalized help. There is a Math/Stats help Centre at Campion College, where you can drop in, and there is Math & Stats support provided by the Student Success Centre. Also, the deparment of Mathematics and Statistics keeps a list of paid tutors at the department office CW307.14.**Academic Misconduct:**by signing up for a class, the student is assumed to be aware of the university regulations; in particular, those that concern plagiarism and cheating, as defined in Section 5.14 of the 2016-2017 Undergraduate Calendar, as well as the potential punishments (which range from a grade of zero in the assignment or test, to expulsion from the University).**Accessibility:**students with a disability who may need special accommodations should contact the Centre for Student Accessibility.**Audio and Video recording of lectures:**this is not allowed, unless you get specific permission of the instructor for cases where needed for accessilibity.**Dropping the class:**please note that*non-attendance does not constitute withdrawal*. Unless you drop the class explicitly (through UR Self Service or through the Registrar's office), you are still considered to be registered, you are liable for the tuition, and you will receive a failing grade of NP ("no paper"). Dates:

Last day to drop the class and receive 100% refund January 18, 2017 Last day to drop the class without a transcript record January 18, 2017 Last day to drop the class and receive 50% refund February 1, 2017 Last day to drop the class without a failing grade March 15, 2017