Dr. Jonas Salk, celebrated medical researcher, has declared that mankind is entering a new epoch. Up to now in the history of modern medicine and previously, our energies have been devoted to extending the duration of our lives. Indeed, we have succeeded very well. From a life expectancy of only 30 years or so in the middle ages, to one in the 60's about 1900, we now have a life expectancy of more than 70 years.
At the same time, the developed nations of the world have seen enormous economic prosperity. Not just in the US, but Europe, many parts of Asia, and Australia have seen great leaps in the standards of living. Because of the prosperity, many of you will retire by the time you reach my age, 57.
Thus we enter the new epoch. Instead of stressing the increased duration of life, we are going to devote our energy to increasing the productiveness of the extra 20 to 30 years with which we find ourselves. What you do with those years depends on decisions you make and experiences you have now. Will you have a life of leisure filled of tennis, golf, television, movies, and fishing? Or will it be a life full of travel, volunteership, reading, college courses and the continued learning of new skills, finding new hobbies, and filled with physical, intellectual, and spiritual growth? I promise you that if you develop in college the joy of training your mind and the confidence to challenge yourself intellectually, you will continue a life full of leaning.
This is why I feel it is important that you not only learn the content of the course, but also that you learn how to learn. Most of you could learn the material simply by hearing me read it to you from the text. But you would not then be prepared to learn a new discipline without the help of a teacher; you would still need to have it read to you.
Success in learning mathematics requires effort. There are three important aspects of learning mathematics. First, getting the idea or the concept (like the following: the zero product principle, ZPP, which states that the product of a pair of real numbers is zero if and only if at least one of the numbers is zero). I can help you with ideas like this in the lectures, and indeed, that is how I see my main responsibility to you. But you can be sure to achieve a deeper understanding by reading the text. Second, you must practice the skills you hope to develop and need for the tests. Without this skill development, the understanding of the concepts will not get you very far. Here the text is especially helpful. You must do the homework problems in the text. The third aspect of learning mathematics is the assimilation process which enables you to recognize ideas you have encountered in other contexts and gives you the confidence to make the leap to solving problems, the likes of which you have not seen before. This is where the Problems of the Week come in. These are not routine exercises. They are problems whose solutions depend of trying something new.
Also, see Dan Kennedy's essay for more on this.