Prologue

As you begin your studies as a university student you are entering a new world; one that is different from the world you have known. A university is not just another kind of high school; one offering more advanced courses than those in the twelfth grade. A university represents an entirely different kind of environment and will call upon you to work in a new way. You are entering a new culture and your success depends upon your willingness and ability to adjust to this new culture. One of the tasks facing your instructors will be to help you make this adjustment and you should cooperate with them as they try to help you.

Quite understandably, you may feel some anxiety about the mathematics courses that you will have to take in your university studies. How will you cope? Will they be too hard? Will they fit seamlessly with the mathematics courses you have had in the past or will you discover a gap that needs to be bridged before you can study the new material successfully? Will the instructor explain the material clearly enough and slowly enough for you to learn it? Will the examinations be fair, allowing you to show what you know?

Perhaps you wonder whether the anxiety that you feel is an indication that there may be something wrong with you. But if you experience mathematics anxiety then you are in good company. Those who claim that mathematics is easy are either lying or so much time has elapsed since they last did any that they have forgotten how hard and demanding it is. It is also intimidating. Everyone, from the students who struggle with elementary mathematics to the distinguished professors who occupy the most prestigious positions in the mathematical community; everyone regards mathematics with a healthy respect tinged with a little fear. Your mathematics instructor knows more mathematics than you do and will be well acquainted with the material that he or she will be teaching you and will therefore be able to explain it effortlessly and fluently. But that does not mean that your instructor is comfortable with all of mathematics. No matter who we are, every one of us has a frontier to our understanding. When we think about the mathematics at our own personal frontier then we are just as scared as you are.

Thus there is a very simple remedy that will overcome much of your mathematics anxiety and help you to do well in your mathematics courses. Since every person struggles at his or her frontier of understanding, all you have to do, in order to succeed, is to make sure that your own frontier is beyond the level of the questions that you will be answering in your examinations. The courses that you will take are designed to help you do just that. These courses are specifically tailored to your needs and to the level of understanding that you are expected to have as you enter them. Your instructor is not trying to trap you; nor will you be required to come up with a burst of inspiration under the pressure of an examination. Your examinations will not torture you with tricky questions or brain twisters. Instead, they will be designed to give you the opportunity of showing that you have learned the material of your course. If you have studied the material then you will find the examination questions to be routine, asking you to solve problems that you have solved before and can solve again with confidence.

One last comment before we leave this prologue: You will notice that this prologue has said nothing, so far, about enjoyment of the study process. Will you enjoy your study of mathematics. Yes you will; some of the time. It will be the dearest wish of your instructor that you should enjoy your studies as often as possible and feel that sense of pride and achievement that comes from an understanding of mathematical ideas. But you will not enjoy all of your studies all of the time. It simply isn't possible. There will be times when your studies are dreary, times when they are painful, times when they may even be a little frightening, times when you will have no idea why your instructor is choosing to present certain material to you. So you won't be having fun all of the time. We offer you no instant gratification. Please understand that success in this life depends upon your willingness to persevere with a task even when it isn't fun and even when it is painful or frightening. When you are done, the sense of pride you will feel in your achievement will more than compensate you for the work you have done.

A Blueprint for Student Success

Introduction

Your success in your studies is not the sole responsibility of your instructors. It is primarily your responsibility. It is your responsibility to make sure that you are properly prepared for each course that you take and that you can afford to devote enough quality time on a regular basis to ensure that you make a proper effort to study the material. Read the following paragraphs carefully and take them seriously.

Conducting Yourself as a Student

Your instructor is a highly trained and highly skilled and dedicated professional whose level of expertise extends to the frontier of knowledge in the material that he or she is teaching you. Furthermore, your instructor cares deeply about your success and has spent many years of his or her life wrestling with the difficulties that are presented both to instructor and student by the kind of course in which you are enrolled.

From a standpoint of ignorance of the material, ignorance of where that material is leading and ignorance of how your present studies relate to more advanced study inside or outside of mathematics, you are not in a position today to pass judgment on the contents of your courses nor on the way in which they are examined. The knee-jerk subjective opinions that you may hold today could well be very different from the opinions you will hold two years from now when you understand more about the role that your present courses have played in your longitudinal development. Place your trust in the professional expertise of your instructor and do the work of the course. You have come to university to learn; not to pontificate.

Being Prepared for Your Courses

The very nature of mathematics dictates that each mathematics course you take must rely upon the understanding of mathematics that you are suppose to have attained in your earlier courses. It is not good enough for you to have official credit for those earlier courses. If those earlier courses are prerequisite to your present course, that means that your present course depends upon your knowledge of the material in those earlier courses. Moreover, your present course is probably more advanced than the earlier courses and will expect you to be able to work rapidly, painlessly and correctly with all earlier material leaving the force of your concentration available for the new material that you are about to study.
The ease with which you will cope with your first university course in mathematics depends, more than anything else, upon the quality of the mathematics that you studied in the twelfth grade. If you made the tragic mistake of not doing very much mathematics in your twelfth grade then it may be necessary for you to take a refresher course on your high school material in order to ensure your future success. You might consider hiring a good tutor for this purpose but, be warned, there are more quacks out there than tutors from whom you would actually learn something.
Knowing that many students in a class are unprepared to a greater or lesser degree, your instructor will make every attempt to help you bridge whatever gaps that may exist. But it is not your instructor's responsibility to ensure that the gap has been bridged. It is yours. Your instructor will be walking a tight-rope, trying to bridge the gap as much as possible for students who come into the course unprepared, and yet, trying to cover the material of the course well enough to ensure that those students who will be progressing to the next level will not have to bridge another gap there. Try to understand that, in a class of thirty five students, there are many different needs. Satisfying all of your needs may mean satisfying fewer needs of other people.
You should understand that, in general, university study is more demanding than high school study and that it includes more advanced and demanding material. In order to be a successful university student you should normally be someone who managed well in high school and who retains the knowledge that was achieved there. Sometimes, however, a student blooms late. That's fine but don't forget that the earlier material still has to be studied. If you ignore it then it will eventually come back to haunt you and will interfere with your studies like a festering sore.
You may believe that the greatest single factor in your success or failure as a university student is the quality and care that you receive from your instructors there. In fact, the greatest single factor in your success as a university student is the quality of the interaction that took place between you and your parents when you were a little child.

Adjusting your Lifestyle

Being a student is a full time and difficult job. It is a sad reality of life that many students are compelled to seek employment while they are enrolled at a university. If you have to work for a living then be aware that conditions in your life are not ideal for study. Do not expect to be able to work long hours at your job and also take a heavy course load. You would serve your interests better if you took only a few courses at a time and worked properly at them with real intent to know and understand the material.
Did you work during term time when you were in high school? Only in the most extreme circumstances should a high school pupil take a job. Not only should a high school pupil not take a job, but the home life of a high school pupil should be set up in such a way as to minimize or eliminate his or her obligation to do household chores. The pupil should be busy enough with the study process.
Are you sleeping enough? One of your obligations as a university student is to go to bed at a reasonable time and to sleep eight hours every night. You need to enter the lecture room wide awake and able to devote your best concentration to the material that is being provided there.
Are you using drugs or alcohol? If you are then you are making it virtually impossible to succeed as a student. If you have experimented with drugs even once in your life then you already have one strike against you. You should also know that some types of drugs, including many stimulants, are known to cause permanent brain damage with just one or two high dosage uses or with a large number of low dosage uses; brain damage that may not show up in many walks of life but could well affect your ability to cope in a demanding mathematics course.

How to Approach Your Studies

This section will sum up many of the basic principles that should guide you in your quest to become a successful university student. Read these instructions careful and resolve to follow them.

The most important principle that should guide you in your studies is that the purpose of your study is to enable you to understand the contents of the lectures that you attended in the classroom. Part of the mechanism of understanding the material contained in those lectures is the doing of homework problems. Thus, one does homework problems in order to understand the lectures. Do not make the mistake of thinking that the homework problems are your primary objective. In other words, do not make the mistake of thinking that the purpose of your lectures is to provide you with instructions for doing homework problems Use the homework problems as a tool to help you understand each lecture.
Do not expect to attain complete understanding of the material while you are actually in the classroom. No one learns mathematics by hearing someone else talk. As a matter of fact, no one learns mathematics by reading a book or by reading lecture notes. As important as all these things may be, they are only steps in the process. You will achieve understanding only when you write out the material yourself, closed book; or when you explain it to others.
If you enter a lecture having made a proper study (including closed book rewriting) of the material of the preceding lecture, then you will find it easy to understand the present lecture. You will find it easy to remain alert. You will find it easy to exit from that lecture in a good position to study its contents properly before the next time that the class will meet. If you walk into a lecture with, at most, a vague and scattered knowledge of the preceding lecture then you will not understand what is being said. Don't blame your instructor. It's your fault. You will exit the lecture with virtually no knowledge of what was done there. You will find it difficult and painful to attempt to study the lecture notes. You will be tempted to avoid studying the material altogether and, instead, look for some ways to remember ``what he wants'' with those homework problems.
Do that and you are on the road to failure.
Attending class is an absolute must. Do not schedule other appointments during your lecture time. You must be in the lecture, both in body and spirit for every minute of every meeting of the class. If you are prevented by illness from attending a lecture, look upon that event as a potential disaster in your life; something that requires urgent and intense action in order to mitigate the damage that your absence has caused.

If you miss a class, do not make the tragic error of asking what homework problems were assigned on that day. Ask, instead, for a copy of the lecture notes. Get a good, readable and reliable copy and work though it carefully and diligently until you have caught up on the material. You have caught up when you know what all of the words mean, understand how the problems there are solved and can reproduce the material of those notes closed book.
Beware of group work! It can be dangerous. Group work can be a good thing but it should be the start of the study process, not completing of it. If one member of a group is dominant and does most of the talking then that one person will do most of the learning. So, if you work in a group, make sure you do the talking; at least some of the time. Then leave the group and do the work again alone closed book to make sure that you know it.
Remember that, in an examination, you are expected to work closed book and it is you alone who does the talking. Don't impose a double standard upon yourself. If you decide, with the notes open in front of you that it ``looks all right'' and then you have to produce the material yourself closed book in an examination then, of course, you won't cope. A common complain we hear from students is: I studied all of this stuff and I knew it when I was at home but here in the exam I blanked out. You should understand that, in the history of the world, no one has ever blanked out. If you can't answer examination questions then there is only one reason why: You don't know the material. On the other hand, if you can solve the problems and reproduce your lecture material closed book then you will also manage to do so in the exam
In assessing whether or not you understand the material, never be willing to write something merely because you believe that this is what the instructor did in class and that, consequently, this is what the instructor ``will want'' in the exam. Make sure that everything you write is being written because you want to write it; because you understand why it should be there. Don't write what you think the instructor wants to see. Write what you want to say. One of the most common symptoms of student failure is the expressed desire to find what the instructor wants in tests and examinations.
The thrust of your study should not be directed at the midterm tests and examination. It should be directed at your need to enter each lecture prepared for it. Just as you have an obligation to be in control of the material of earlier courses when you are studying your present course, you have an equal obligation to know the material of earlier lectures in order to attend your present lecture. Unlike a typical mathematics class given in a high school, a university mathematics lecture will always cover new ground. Each lecture will be given under the assumption that you have studied the preceding lecture and that you know the material. If special words or phrases were introduced in that earlier lecture then you will be expected to know what they mean. If you don't take the trouble to know what the words mean then nothing you do with them will make any sense.
When you are studying the material that you received in lectures, you are studying both the workings of the mathematics to solve each problem and also the correct way to lay out your solution in meaningful and readable language and notation. You can expect the presentation of each solution as given by your instructor to be in precise and meaningful language and you should strive to match that precision. Remember that there is no point in writing anything down unless that thing can be read. Apply the same standards at all times. Something you write down on a scrap of paper that will be consigned to the recycling bin should be written as carefully and fully as anything you are submitting to an examiner for a course grade. Don't apply a double standard to yourself.

Consider: if you are learning tennis, you wouldn't hold the racquet in your teeth during practice and transfer it to your hand only when to arrive at the centre court at Wimbledon, would you?? So don't do that with mathematics.

Summing Up

As you can see from what you have read in this document, we offer you no instant gratification. We know of no short cuts. We know of no path to success other than dedicated and diligent hard work and a desire to succeed.

Perhaps, if all of the message of this document is to be summed up into a single statement then that statement should be that you can succeed if you really want to succeed; but you have to be serious about that wanting.

If you work correctly then you will find that the demands made upon you by your studies will not require you to be a genius. In fact, many of the most successful students are people who have reason to believe that they are not at the top of the heap when it comes to talent or intelligence. There is something else that matters much more: the will to succeed and the willingness to do what it takes to reach that goal. If you work for success and care about yourself then you will make it easy for us in the university to care about you and to work with you to help you succeed with your quest.