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"Do not worry about your difficulties in mathematics, I can assure you mine are

"Do not worry about your difficulties in mathematics, I can assure you mine are still greater." - Einstein MATH SURVIVAL GUIDE FOR FIRST YEAR STUDENTS UTSC MATH & STATS HELP CENTRE Compiled and edited by Geanina Tudose CONTENTS 1. What is university math like? 2. How to be a great math student 3. Problem Solving 4. Writing mathematics (homework and tests) 5. Preparing and taking a math test. Dealing with anxiety 6. Getting Help 7. Appendices:  FAQ (Common Student Concerns)  TLS Support  Additional Readings Teaching and Learning Services Math & Stats Help Centre University of Toronto at Scarborough ©2004 TLS 1. What is university math like? What is new and different in university? Well, almost everything: new people (your peers/colleagues, teaching and lab assistants, instructors, administrators, etc.), new environment, new social contexts, new norms, and – very important - new demands and expectations. Think about the issues raised below. How do you plan to deal with it? Read tips and suggestions, and try to devise your own strategies. First-year lectures are large – you will find yourself in a huge auditorium, surrounded by 300, 400, or perhaps even more students. Large classes create intimidating situations. You listen to a professor lecturing, and hear something that you do not understand. Do you have enough courage to rise your hand and ask the lecturer to clarify the point? Keep in mind that you are not alone – other students feel the same way you do. It’s hard to break the ice, but you have to try. Other students will be grateful that you asked the question – you can be sure that lots of them had exactly the same question in mind. Lectures move at a faster pace. Usually, one lecture covers one section from your textbook. Although lectures provide necessary theoretical material, they rarely present sufficient number of worked examples and problems. You have to do those on your own. Certain topics (trigonometry, exponential and logarithm functions, vectors, matrices, etc.) will be reviewed in your first-year calculus and linear algebra courses. However, the time spent reviewing in lectures will not suffice to cover all details, or to provide sufficient number of routine exercises – you are expected to do it on your own. 2 You have to know and be proficient with the material from  Basic Algebra  Basic Formulas from Geometry  Equations and Inequalities  Elements of Analytic Geometry. For instance, computing common denominators, solving equations involving fractions, graphing the parabola y=x2, or solving a quadratic equation will not be reviewed in lectures. In university, there is more emphasis on understanding than on technical aspects. For instance, your math tests and exams will include questions that will ask you to quote a definition, or to explain a theorem, or answer a ‘theoretical question.’ Here is a sample of questions that appeared on past exams and tests in the first-year calculus course:  Is it true that f’(x)=g’(x) implies f(x)=g(x)? Answering ‘yes’ or ‘no’ only will not suffice. You must explain your answer.  State the definition of a horizontal asymptote.  Given the graph of 1/x, explain how to construct the graph of 1+1/(x-2).  Using the definition, compute the derivative of f(x)=(x- 2)-1. Mathematics is not just formulas, rules and calculations. In university courses, you will study definitions, theorems, and other pieces of ‘theory.’ Proofs are integral parts of mathematics, and you will meet some in your first-year courses. You will learn how to approach learning ‘theory,’ how to think about proofs, how to use theorems, etc. Layperson-like attitude towards mathematics (and other disciplines!) - accepting facts, formulas, statements, etc. at face value - is no longer acceptable in university. Thinking (critical thinking!) must be (and will be) integral part of your student life. In that sense, you must accept the fact that proofs and definitions are as much parts of mathematics as are computations of derivatives and operations with matrices. ©Mathematics Review Manual, Miroslav Lovric, McMaster University, 2003. 2. How to be great Math Student These remarks are provided to assist you, the first year student, in making the transition from high school to university. For a student with intellectual curiosity who is determined to work regularly from the beginning of the term, 3 a first year mathematics course can be remarkably rewarding and stimulating. However, the unwary student may fall into difficulties and have a poor experience instead. These following are intended to help you avoid that. 1. In all mathematics courses, the key to success can be summarized briefly: DEVELOP REGULAR WORK HABITS SO YOU DO NOT FALL BEHIND! This will ensure that you develop the depth, breadth and maturity of your knowledge. It means: attend lectures and tutorials, do assignments and enough extra problems to master the material. If you attend lectures, but don't do exercises, you may get lulled into a false sense of accomplishment and can expect a rude shock. In mathematics a thorough knowledge of the previous material is essential to reach an understanding of new material. Hence, falling behind tends to be cumulative and is one of the most frequent causes of failure. Understanding grows with time and experience. Do not expect to follow the mathematics completely, right away; you will have to think about it, and it may not be until later work is covered that you can appreciate the full significance of earlier material. 2. Some of the ideas in many first year courses, such as differentiation, have been introduced in high school. This does not mean the course is a review. New and more sophisticated concepts will be introduced and must be mastered at a new and higher level of thoroughness and understanding. 3. Learn from doing badly. If you receive a poor grade on early tests or assignments, that is an important signal that you are not mastering the material at an appropriate level. You can deal with this by working harder and consulting about problems with your TA or instructor. 4. If you are having difficulty, first consult your TA; then if the problems persist, your instructor. Professors have regular office hours and are generally willing to meeting with students outside these times by appointment. It should be emphasized that it is your responsibility to seek help if difficulties arise. 5. The Math & Stats Help Centre AC320 and the Math Aid Room S506F is open for extended periods and staffed by faculty and TAs who will assist you. The Math & Stats Help Centre offers tutoring, study groups, and workshops on study techniques and seminars on various mathematics topics. More detailed information can be found on the centre’s website. 6. Do not delay asking for assistance until the day before the exam. It is impossible to cram mathematics at the last minute. Just as with playing a musical instrument, learning mathematics involves a development of skills and understanding that must be consolidated over a period of time. 7. One of the main differences between high school and university is that, at the university, you are expected to be responsible for mastering course material. Considerable help is offered--lectures, tutorials, mathematics assistance centres and personal help--but it's your responsibility to utilize it. 4 8. If, nevertheless, you find that you have fallen behind in your coursework, speak with your instructor. He or she can advise you on what to do next. 3. Problem Solving Problem Solving (Homework and Tests) The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece divide and conquer!  Problem types: 1. Problems testing memorization ("drill"), 2. Problems testing skills ("drill"), 3. Problems requiring application of skills to familiar situations ("template" problems), 4. Problems requiring application of skills to unfamiliar situations (you develop a strategy for a new problem type), 5. Problems requiring that you extend the skills or theory you know before applying them to an unfamiliar situation. In early courses, you solved problems of types 1, 2 and 3. By College Algebra you expect to do mostly problems of types 2 and 3 and sometimes of type 4. Later courses expect you to tackle more and more problems of types 3 and 4, and (eventually) of type 5. Each problem of types 4 or 5 usually requires you to use a multi-step approach, and may involve several different math skills and techniques.  When you work problems on homework, write out complete solutions, as if you were taking a test. Don't just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don't just do some mental gymnastics to 5 convince yourself that you could get the correct answer. If you can't get the answer, get help.  The practice you get doing homework and reviewing uploads/Litterature/ survival-guide 3 .pdf