UW-Milwaukee - Department of Mathematical Sciences

UWM Mathematical Sciences

Center for Interdisciplinary Mathematics (CIM)

International Conference CMMSE

Regional Conference MWNADAY

Professor B. A. Wade

wade@uwm.edu
www.uwm.edu/~wade
414.229.5225

For Students of Mathematics & Statistics

Comments on Computational Mathematics

Undergraduate level: Matlab (check the student version), O-Matrix (Windows), or Octave (public domain, Windows and Linux) are excellent programs to do anything you need. I find, personally, that symbolic platforms are not totally essential because when you actually examine what you are doing with it it turns out to be graphical or estimation. If you can't calculuate something symbolically by hand, it is often too complicated to use the output of a program like Maple or Mathematica. In my mathematical modeling course it often turns out to be more convenient to use spreadsheets, or some combination of spreadsheets and Octave. Here is a web page with Matlab/Octave information and examples. Here is a web page with an Octave tutorial.

Graduate level: My graduate students often have the experience of running into difficulties from too much dependency on interpreted programming environments rather than creating their own compiled code. When computing, decide ahead of time what computational complexity you expect in the the end. Students often make the mistake of using packages like Matlab, Octave, Maple, etc., because it seems much easier to start and protype algorithms. Often, they start well but end disappointed because the object of the computation, once all debugging is done, is too challenging for these slow interpreted platforms. I always note that the difference between writing your own code in C, C++ or Fortran and, say, Matlab, is not very significant. The computational experiments at the end will kill you if they take days or weeks per experiment rather than hours! For this reason, I recommend that you start with the programming language C or Fortran even if it seems more difficult to set the data structures.

I prefer Fortran for its simplicity in programming yet powerful capabilities. Fortran (2003) software repositories are available on this link.

Here is a web page with Matlab/Octave information and examples. Here is a web page with an Octave tutorial.

Here is a web page on GFortran, a good linux package for modern Fortran (I use Ubuntu).

Gnuplot is an excellent graphics program to go along with Octave or Fortran.

It's Essential to Get Organized!

There is a near crisis we all seem to be experiencing these days from society that has gone digitial and become extremely organized and systematic about just about everything. People are becoming more anxious, even unable to function, from the stress of it all. And they wonder why, but don't actually doing anything about it. How to manage?
You need to "fight fire with fire." That is, when every institution around you is becoming hyper-organized pay attention to the system and put yourself in sync with it! To do that be organized (or even hyper-organized) yourself, at least with the items that are relevant. By writing everything down it is not in your head and you can relax. Be sure to keep a significant part of your life without a system, living emotionally or intuitively on your own free time, or you will go crazy eventually.

Estimate the time it will take for projects, a project is anything that consists of more than one task and a task is anything that can be done in about a half hour. Keep track of all your projects on paper or electronically. Most people underestimate the time it takes, so leave more time than you think you need.

You must keep a record book, PDA, computer files, etc.- some sort of system- for all the passwords and user names that seem to constantly barrage us. You should carefully keep a calendar of some sort that contains all your obligations. And review it every morning to avoid forgetting things you have to do. Once a week reset this plan.

Depend on the "WADE" formula:

"WRITE IT DOWN" Record your tasks in single place in an organized fashion.
"ADD IT UP" Estimate the projects' time frames and write that down. Set priorities.
"DECIDE" Work out if you should do the next task of a project immediately, delay it, delegate, delete it, etc.
"EXECUTE YOUR PLAN" Make a daily task list, making sure that the tasks are not whole projects but shorter, viable activities. Be realistic!
cf. Julie Morgenstern, "Time Management from the Inside Out," Holt Paperbacks, 2000.

A very popular and excellent resource on organizing yourself is by David Allen: "Getting Things Done: The Art of Stress-Free Productivity," Penguin , 2002.

Winning* the Game of Life

Students! Don't wait for the test to find out what you don't know! What kind of approach to learning is this? It appears random. Get a plan. Start to care more.

You are at college to qualify for and enhance some professional career...Therefore, you now are a professional; at this time you are being paid on "futures," nevertheless you need to act like a pro. That means, do the job right, on time, without complaints or excuses, and manage yourself properly.

Life is a series of 'games', many of them played simultaneously and some are voluntary, some not. A game is an activity with rules, strategies, usually teamwork, and a measure of degrees of success or failure. Often, there is a time limit, and often you must prepare beforehand in a dedicated and organized fashion in order to really be good.

Many people have trouble from the the fact that they do not know they are the games or they have accidently wandered onto the wrong field. When your peers are playing by a certain set of rules different from yours, you can not win. Some games are not up to you, but a lot are your choice. And people play dirty and you have to be ready for that, too.

Be careful not to accidently walk onto the wrong playing field, with rules and tactics not to your expectation, above your ability, or, worse, of which you are not aware. Be sure to consciously choose the games you play, to the extent that it is possible. That way, the rules, tactics, goals, and ultimately the measures of your performance will be much more natural. You will be happier and more successful.

The beauty of this is that when you take yourself out of a game there is no longer any measure of 'you,' it makes no sense to think of yourself as good or bad. What a way to avoid stress!

Many people suffer from not understanding the goal of the 'game' they are playing. Think deeply about it; when you realize what you are about as opposed to what you think people are telling you to do it will make a tremendous difference. Your frustration level will decrease and you will grow satisfied with the work you are doing.

Commonly, in your 'game' others are playing with different tactics or rules of engagement...they play 'hardball' against your 'softball.' Again, think deeply about it. If 'softball' is your desired game, let them have their fun and continue the way you see things. But you must decide ahead of time to be satisfied with your decision and not second guess yourself based on others' attitudes. Once you've decided clearly to do the right thing, to play the right way, the competition's 'cheating' won't bother you, as you will be confident and satisfied in your own self.
By the way, experience tells us time and time again that overly 'aggressive' or 'cheating' players, those taking short-cuts, and non-team players eventually lose out. You, however, doing it the right way, playing with team spirit, will succeed through preseverence, hard work and attention to detail and quality.
What are the handicaps or constraints you are 'playing' with, for example, family obligations, extra job, health issues, or perhaps unwillingness to 'play' nasty? Or, how about a desire to have a complete life and not be so focused on work that you missed out on living? Compared to others who are getting ahead, if you play with one arm tied behind your back, and 'lose' the game but with a hard fight, who really won? Don't fall into the other guys' trap of glorifying them because they 'beat' you, forgetting about the constraints you are playing with.

When you realize you are in the wrong game (either the rules are too harsh, the tactics too dirty, the measures not good for you, etc.) you don't have to quit. Simply keep playing but readjust the rules, tactics, measures to your liking. This will have the effect that you keep on performing but with more relaxed style and better enjoyment. If the others claim to "win" because you stopped playing their game just remember that they did not not actually win because when you changed the measure their idea of winning ceased to have meaning relative to you. Even if no one notices you are playing differently you are less stressed and happier.
An example: You are in a course and it seems that your peers are trying very hard to do better than you, that they are putting themselves forward aggressively and the professor seems to respond to that. You hate this and the whole course starts to go down the drain for you. What to do? Well, change the "measure of you" and the tactics. How about deciding consciously that the others can have their A grade but you will keep on learning the material as best you can, that what YOU learned is your measure of success, not any grade or score. I am confident that you will before long start to relax and learn a lot, noticing that you like the class better. You will not be worried about the other students but only yourself. And perhaps you will ace the course and they won't.
An analogy: Every soccer team has a star forward who scores and gains the glory. Did you ever notice how they rest and let you defenders work very hard without any glory? You defenders are looking all around, covering the field and heading off all potential danger, sacrificing your body for the cause, and helping on the offense, too. Many have argued that defense wins championships. Is it like this for you at school or work, that someone seems to always claim the credit while acting like a prima donna? Just change the measure in your game, and remember that a team (like your work place) cannot win without the defenders. Keep it up and eventually they will notice how good you are in 'defense.' Defense, of course, is analogous to doing the hard, everyday work at the office, and the forwards are the ones doing less and receiving the accolades. Don't worry. Don't be jealous. Be serious and hard working.

Ancient wisdom of various sources (Eastern & Western) tells us it is better to live in the present moment. The past is overwith, and the future, although important, is mainly a source of anxiety. How to tackle this beast of worry called the future?
Just realize that the future needs to be accounted for by organizing your goals, motivations, and activities. Not emotionally, rather more calculated. Make a plan, perhaps every hour, day, week, month, year, depending on your lifestyle and personality. The plan should be written and well-organized if possible. You must remember that it is only a recommendation to yourself, that you are simply readjusting your course at the moment to remain with good overall progress as the winds of life carry you off track. That is, it has to be flexible or it will be a new source of anxiety. You will need to revise the plan often to account for changing events or motivations. Without a goal you go nowhere.
Now with your concentration and emotions focused on the present moment you practically zero anxiety, only effort or enjoyment, etc.

Living in the 'present' means relative to space and projects, too. A common impediment to success for students, for example, when writing a thesis, is to worry about the end before the beginning. If you have a project that will extend a long time, do not make the mistake of overly thinking or agonizing about the outcome. Rather, organize and plan the outcome in a general way, though not too specifically because you don't know all the bends and turns the project will take as it is developed.
For example, suppose you are an NFL quarterback in the first game of the season. You are worried about wining the Superbowl, so on the first play you through all the way down field. You will very shortly be taken out. To win the Superbowl you must remember that you have to go step by step, and there will be loses and setbacks. You have to win a lot of games, but first you have to score. Before you score you should get a few first downs. Before that you should make take some yardage. So, to further your Superbowl aspirations, on the first play of the first game you do a running play to gain 3 yards.

To be in the present (spatial aspect) you need to focus. Focus prevents errors through attempt at so-called multi-tasking. Many people make the mistake, even brag, about trying to multi-task. It is impossible, all they are doing is double timing actions, to the detriment of the quality of the product!

*'Winning' is not what many think. Again, ancient wisdom tells us that sometimes losing is winning. If you lost a game, did you learn something or find a weakness? Did the winner gain anything, other some artificial, temporary good feeling? The who honestly won? When 'losing' did you support your 'teammates' and make good friendships? When 'winning' did the other guy cheat, bend the rules, injure someone, show a bad attitude? Is there EVER any value to competition other than the process, the improvement you gain, the enjoyment and camaraderie?
Nothing new here, right? Pretty obvious for sure. Well, it seems that everybody has the idea built-in that winning in competition, vanquishing the opponent, is the absolute goal, the only one that matters. It's that our social structure values glory, wealth, and domination. Honestly, most of us do not have the personal fortitude and strong character to resist going the wrong way (trying to win at all costs).

Are these ideas not effectively reinterprations of H.D. Thoreau's point of view? Consider:
"Pulic Opinion is a weak tyrant compared with your own private opinion. What a man thinks of himself, that is which determines, or rather indicates, his fate." - Henry David Thoreau, "Walden" (I.e., Remember that other people make the tactics and rules, often not what you want. Design your own game.)
"Man is the artificer of his own happiness." - Henry David Thoreau, journal entry Jan. 21, 1838 (I.e., Choose the game you play, get out of a bad game and there is no longer any measure of you, good or bad. You are happier.)
"Any fool can make a rule, any fool will mind it." - Henry David Thoreau, journal entry Feb. 3, 1860 (I.e., Don't foolishly walk into the wrong 'game' for you, whose rules are made by someone else's false or limited priorities.)

Making Decisions

When there is a decision to make, use intuition over logic. Logic or 'pro-con reasoning' is only as good as the measure you choose, i.e. the weights on relative importance of the choices. These weights are usually given arbitrarily with little thought, yet they make the decision for you! Because of the modern world we live in we fall so easily into this trap, that it is possible to make an analytical/quantitative based decision. Yet, it is impossible to identify and quantify all the variables and constraints, not to mention anticipate the future consequences.

A better way to decide: I) If it is not of major importance just use your gut feeling and make a relatively quick choice, but live with it once it's decided. II) If the question is obviously very important, take more time and use my method, which I call 'Dynamic Visualization.'

The idea of the method of Dynamic Visualization is based on the fact that a 'pro-con-list' style decision has the flaws of 1) weights for importance of things are usually arbitrary and inaccurate or based on what other people think; and 2) it is static, it looks at the here and now, whereas an important decision has time evolving consequences.

Dynamic Visualization is this: First list the decision branches. Then using intution more than analysis, spend some time (one day maybe) imaging that you have already decided on 'A,' say, and project the consequences of that decision into your future. Do write notes down to remember the ideas that flow into your head, but be sure to let imagination and intuition dominate. The next day (or next hour, perhaps) imagine instead that you had chosen 'B.' Now work out intutitively all the consequences of that choice. Write notes. Continue in this way until you work throug all the options. Visualize the future consequences of the decisions.

The important thing to realize about this dynamic approach is that with it you consider (intuitively) the future consequences of your decision rather than the static current ones. Your gut feeling will assign the weights and importance to various events or consequences, most likely better than if you tried to do it explicitly. Obviously, a serious and difficult decision is important because it affects you in the future!

Enhancing Performance with Visualization

Visualizing your activity, imagining some thing you did badly (before) now replayed with you doing it well, or picturing the solution to the problem without getting bogged down in details, can be very valuable and is well established by psychologists to work. Sometimes we need to take advantage of the advice 'work smarter, not harder.'

It is not well known, but the mind plays a truly important role in performance and problem solving. There are many situations that call for quick, automatic reactions. Highly experienced 'players' have seen these 'problems' previously and have worked them out from repetition. Not everyone has this advantage, but you can improve performance by imagining the tough situations and then working out in your mind by visualization the way you should handle it to be excellent. Vary the mental picture; 'feel' the imagined situation as if it were real. See yourself doing the right thing, well.

For example, psychologist A. Richardson chose three groups of students at random to take a test of free throw percentages in basketball. None knew about the techniques of visualization. The first group practiced free throws each day for twenty days. The second was tested with free throws on the first and last days but did nothing in-between. The third group was also tested the first and last days, but instead of physically practicing spent 20 minutes each day visualizing shooting free throws.
On the twentieth day the percentage of improvement for the group that practiced daily was about 24 percent. The second group did not improve at all. The third group, which had only visualized improving but did not actually practice, did about 23 percent better!
Richardson's article in the Research Quarterly mentions that the most effective visualization happens when the person feels and sees what he/she is doing (http://www.llewellynencyclopedia.com/article/244). You can search the internet for many such examples and related ideas.

Get Smart! Learn from Cats.

Cats depend on intuition.

Cats thrive on exploration and learning. They learn by trial and error, observation, and imitation. Instinct/intuition guides them as well. Cats learn best by breaking the process down to small incremental steps. They are naturally curious and, by the way, curiosity never killed anything other than a little time.

Cats know the value of being relaxed but always alert, and they usually do not let themselves get stressed by outside forces.

They like to have fun and they do not let themselves become so serious as to forget to enjoy life. They don't need fancy toys.

Cats are not afraid to leap to great heights- or fall down. However they always look before they leap.

They instinctively know when to quit, when it isn't worth pursuing. On the flip side, they are also very patient, clever and stealthy when hunting.

Cats are never sleep deprived, they nap adequately to make sure they're always at top of their game. They manage themselves well.

Cats stretch frequently and keep fit through exercise, but not mindless, repetitive exercise. Rather, they exercise through fun and games or personal challenges. And they don't over eat.

They only use their claws when necessary. Sometimes they do use them, and they are sharp.

Most importantly, cats are not motivated by social status!

Some of My Interests

Amateur (Ham) Radio. My radio amateur call sign is N9UR. I have been licensed since 1975, licensed as extra class since 1977.

I participate in soccer where I manage an over 40 men's team, BD Chaos, (indoor & outdoor), I like to work out in good weather by in-line skating, biking (road and mountain), and kayaking. I manage to remain able to do these things by regular yoga practice. Of all these the yoga is most difficult for me, as I have neglected to work on flexibility and balance most of my life, besides the fact that this is a very challenging style.




Salamanca, Spain. Thanks to my good friend J. Vigo-Aguiar, I was able to live and work on research in Salamanca Spain for 7 months during 2005. It gave me an opportunity to use my sabbatical to learn new things, mathematics, spanish, and living with a different life-style. I always try to go to Spain whenever possible.


I am an Irish-Certified Whiskey Taster: