How to Study for Physics, Engineering, and Mathematics Classes in College
Stevens F. Johnson

Ask yourself this question. "How do I study for a class? More precisely, how do I get an A, or just a good grade (well, OK, a passing grade) for a class?" Here is one answer:

"Studying? What studying? All I need to do is commit to memory everything the Instructor said in class, what is printed in the textbook, listed on the syllabus, outlined in the handouts, attempted in the laboratory experiments, and rumored to be on old exams (all on the night before an exam). I then merely regurgitate it on the relevant exams. Wait. That's too much effort, unless I'm going for a top-of-the-class A+ (and who needs that?). For an A, I need only an A-. That means I can reduce my effort by 10%, mostly on attendance of the class lecture. Even better would be a 20% cut, that way I can skip the Monday morning or Friday afternoon classes, but make up for it by laughing loudly at the Instructor's jokes and stories or volunteering what I think are coherent and relevant questions in class when I do attend. A grade of B for the course is even easier, since then I can neglect to do a few homework assignments, miss a lab or two, not to mention an exam, or take off a whole week or more for deer hunting or that special October (February) vacation. And a B still looks almost as good on a transcript, I hear. On the other hand, that still requires a lot of effort. A C will let me count that class for the Major, enough to graduate. Anyway, it's worked before, it'll work again. Right?"

All right, I'm exaggerating a bit, but you get the idea. Even so, if I were to reply to the above paragraph, I would say ...

"WRONG! Not in a Physics, Engineering, or Mathematics class (and a lot of other courses, too), at least not if the Instructor has any professional integrity with respect to her teaching and her evaluation of students' understanding of and skill in the subject. (I'm not exaggerating now.) There is not one thing correct in that Paragraph that would help you get a passing Grade, let alone acquire an Understanding of the Subject of that Class."

Does my response come as a shock to you? It certainly would be a surprise to a lot of college students today. (Note: I'm not talking about cheating or behavior unbecoming a serious student. That is a question of Ethics, the topic of a different essay.) There are at least eight Wrong Ideas about studying in that paragraph. I will address all of them, in no particular order. Along the way, I'll be addressing the most common Complaint that I, and most other Science Instructors, have received over the years from Non-Science Majors taking a Lib Ed Science class: "I get A's and B's in all my other classes, but I'm struggling to get a C in this class," or "This is the hardest class I've ever had!"

Memorization?

An outright attempt to memorize this stuff will put anyone to sleep.

Memorization will get you Nowhere in Science, for several reasons. The most obvious reason is there is simply too much to memorize; Any attempt at even a small fraction of it will just get you confused and won't lead to Understanding anyway. Successful intimate familiarity will come naturally from Practice, not from rote memory. After a dozen or so attempts at problems that involve having to solve for the roots of a Quadratic Equation, for example, you will have developed a level of comfort that will be, for all practical purposes, an Effective Memorization of the solution to the quadratic equation "a x-squared plus b x plus c equals zero:" "x equals negative-b plus-or-minus the square root of b squared minus four a c, all over two a."

You may thinking, "Yeah, right. That's easy for you to say. You've been using this formula for years, and it's your business to know it. I'm just an undergraduate hoping to graduate someday." Of course it's my business (and it's decades, not years). But it is your business, too, if you want to graduate with a degree in Physics, Engineering, or Mathematics. More to the point, I had the formula effectively memorized before the end of my Junior year in High School. It was the practical result of many hours of Practice at using it. What do we call those hours of practicing? Studying. Lots of Studying. How much Studying? That is the next subject I will address. But first ...

I want to mention a Caveat to my injunction against rote memorization. There are branches of the Natural Sciences that do require a level of memorization higher than for Physics, Engineering, and Mathematics. Chemistry and the Life Sciences typically have a large upfront Vocabulary that must be mastered early before moving deeper into their respective fields. However, Effective Memorization techniques are just as good for them as for Physics. Instead of just memorizing a list of the skeletal bones of the human body, draw the relative location and size of each bone, and label it, as you verbally list all of them, for example. If you have to peek at the text occasionally while doing this, that's OK. What you would be doing is not memorization, but Studying.

Study Times; Study Timing; Study Planning
Yes, Studying. There is no way to avoid it. What is Studying? It is reading in detail with the intention of learning (Webster's New World Dictionary of the American Language). To read in detail implies you must devote your Full Attention over extended periods of Time. A traditional and generally accepted Rule for studying at the college level is to multiply the number of Credits for which you have enrolled by two to four. The result is the number of Hours per week you should study in addition to your Class and Lab times. For example, for a typical full-time student who is enrolled for 16 credits, she should devote an additional 32 to 64 hours every week to her studies, for a total of 48 to 80 hours for every seven day period. That means, on average, she should be studying about seven to eleven hours every day, including weekends.

Sleeping and reading are best done separately.

"Holy smoke," you may be thinking, "I don't have time for that much studying. And when do I get to play?" Assuming eight hours of Sleep and another three for Grooming and Meals, that still leaves two to six hours for Recreation and Relaxation every day. How much more time for Fun do you need? Personally, I need a break after six hours of Playing. (Alternatively, if you wish to reserve the weekends exclusively for Recreation, you'll have to study about 10 to 16 hours every day Monday through Friday. That would be pushing the limit, in my opinion, and may even be counterproductive. More on that later.) Of course, these are average numbers. They should be adjusted to account for the level and ease (to you) for each class. Still, they are excellent Guidelines.

This general Rule arose from the average amount of time college students studied during the 1950's through most of the 1970's in the United States. Unfortunately, since the late 1980's, there has been a disastrous trend downwards for study time, almost down to no studying outside class for some students. This trend has also been seen at the high school level. It is the basic reason why ACT and SAT scores have been falling for the last three decades, and the fundamental source for the perceived need for Grade Inflation in the Colleges and Universities (and High Schools). See a recent Associated Press news article on Bad Study Habits and Grade Inflation here.

Hence, being a Full-Time College Student is the Equivalent to holding a Full-Time Job, plus ten's of hours of Overtime every week. That means, of course, you really don't have time for a significant job off-campus. "But how am I to afford the cost of college if I can't work?" you ask. There are lots of ways, including Savings, Summer Jobs (which are psychologically good for you, anyway, as a break from nine months of Intense Study), Scholarships and Grants (of which there are many, but you have to go looking for them yourself: Use the Internet. Click here for a short pdf list.), and Student Loans (which have the lowest interest rates and best repayment conditions of all loans, and are available to everyone). If none of these Options are acceptable to you, either you should be a part-time student instead, or you should drop out all together until you can be a full-time student.

It should be obvious by now that waiting until the night before an Exam to study won't make the Grade, so to speak. You cannot cram several Weeks of Study (hundreds of hours ) into one All-Nighter. Even if you could, it wouldn't work. Why? Because Understanding takes Time, lots of Time. And lots of Practice over that Time. Your Brain needs the Time to form the new Neural Pathways and Patterns that are a result of new Understanding and Skills. Learning Science is similar to learning new Plays in Football or Basketball, or learning new Music on the Piano, or a new Play on the Stage. It takes lots of Practice (or Rehearsal) to master something new, to establish the Muscle-Memory (including Mental Muscles) that makes the new Play (or Piece or Skill or Understanding) Second Nature for you.

Continuous Study for any given Subject (i.e., a bit of Study every day for each Class) also can accommodate for those occasional but inevitable times when you hit a Wall, a Mental Block. When the next Exam is still days or weeks away, you have the Luxury of temporarily giving up on the Topic of that Mental Block, to go do something else (anything else: Recreation, studying for another Class, a Meal) for a few hours or until the next day. When you return to the Problem, you will likely be surprised at why you thought it was difficult in the first place. The reason is your Subconscious works on a resolution to your Mental Block while you are consciously doing something different. It still astounds me how a Good Night's Rest will solve a problem that a day before seemed intractable. To avoid Mental Blocks, time your studies for any single Class so that you can spend at least an Hour but no more than two or three Hours at a time on that Class. That way, you move on to something Different before you get mentally tired of it, and you'll still feel fresh to study for the next class.

Up to now, I have only talked about how much Studying you should do and when, but not on specific Techniques. On this point, I can only give you broad Suggestions in general, and specific Examples that have worked for others. You will have to adapt these Ideas to your own Strengths and Idiosyncrasies (which we all have, so live with it!).

Reading
Read the Textbook, a Chapter at a time. Read it more than once. I'm serious. Really. Scout's Honor. It is the single most important part of Studying, more so than attending the Class. I kid you not. Truly.

Multiple Readings should be done on different Days and for different Purposes. For example, the first Reading of a new Chapter can be a Fast Pass Overview, looking at all the Section Headings, the Pictures and Diagrams, the Examples, and the Summary. The Purpose here is to get a feel for the topic of the whole Chapter, the Big Picture, and to do it quickly; It shouldn't take more than half an hour or so. (If the Chapter is very long, break it into smaller chunks at a time.) Don't worry about understanding the new Words and Concepts yet. You are only trying to become vaguely familiar with things on this First Pass. When the new Ideas are introduced in the Lecture, it will then be your Second Exposure to them and they will not seem so new and alien. (Yes, that means you should complete the First Pass, at least, before the Chapter is started in Class. The Night Before will do.)

The Second and Third Pass Readings, with increasing Attention to Detail, should be done while the Chapter is addressed in the Lecture. The Third Pass should be the first where you examine the Calculational Examples (along with those from the Lecture). But don't just look at the Examples. After close scrutiny of each, close the Book/Lecture Notes then try to reproduce them on Fresh Paper. If you have to sneak a peek now and then, no problem. You'll still be learning by doing.

Even though this famous book by Douglas Adams is Science Fiction, the emphasis is on fiction. Read this or another novel quickly if you wish, but not so a science textbook.

A note of Caution: A textbook in Physics, Engineering, or Mathematics is not a Novel. Consequently, do not read it the way you would read a Novel. Do not try to speed read it. Go through a Chapter very slowly, because unlike a Novel (or news article, or History textbook, or Legal Brief for that matter) every word and sentence is equally important. There are three reasons for this. (1) Technical textbooks have very little repetition in their Prose: They generally state a Principle or Fact once and only once. Miss it the first time and you will likely not get a second chance of seeing it on that Reading. (2) Both Facts and Reasoning are presented in the body of a Chapter. It is the Reasoning portion that requires your slow and careful consideration. (3) There are a lot of Equations. An Equation is merely a brief and concise mnemonic for reminding you of the relationships between various physical and mathematical attributes. It has a very high Density of Information per character. Think of it this way: If a Picture is considered worth a thousand Words, then an Equation is worth a thousand Pictures. That's a lot of Ink! So don't try to breeze your way through a million words in a glance.

Textbook authors and Editors are Human, too. There will always be errors in any Book. If you come across a sentence that simply makes no sense, it may simply be an error. Check with another Student or the Instructor, or go to the equivalent section of a different textbook from the Library. On the other hand, don't be too fast to assume an error. Read at least a paragraph or page further into the Book. There may well be a clarifying Restatement or Example.

Homework and Problem Solving; Mathematics
This brings us to doing the Homework. In Physics, Engineering, and Mathematics, this means doing Examples invented by the Instructor or the Text's Author that have not been solved for you. You may or may not know what the Answers are (from the back of the Book), but you still must plow through some Problem-Solving Methods that will lead you to the Answers. The most important Ingredient to successful Problem-Solving is Faith in Yourself. The second is Patience with Yourself. The Faith involves the Knowledge that you really can solve a Problem given enough Patience and Time. The Patience involves being very slow, careful, methodical, and (to Outsiders) boring. There is a Routine that will almost always do the trick:

The famous "Splash is heard 6 seconds later, how deep is the well?" problem. The sketch contains all the information needed to solve it. Note: The solution requires solving a quadratic equation.

1. Read the Problem thoroughly and carefully. Take note of everything that is stated, but do not make unnecessary Assumptions.
2. Draw a Diagram of the Situation, with all the relevant facts illustrated in some manner. (Use a pencil.) This is an extremely important step because it forces you to take a look at the Full Picture and to consider all the given Facts of the Problem. If you have some Trouble understanding what the Problem is asking of you or of some of its Facts, a Sketch or Diagram will help you understand, because Inconsistencies or an incomplete set of Facts will become very obvious as you attempt the Diagram. My General Rule of Problem-Solving is "When in doubt, draw a Picture. If you are not in doubt, draw one anyway, because there's a strong likelihood that you are in doubt but don't yet know it." Go back to Step 1 if necessary. One Caution, however. It is not unusual for the statement of a Problem to seem not to have given you enough Information to solve it. Here, you may have to begin depending upon the Faith and Patience I mentioned earlier.
3. Write down what you know, what you don't know, and what you need to know about the Problem. This includes Equations (the more, the merrier), Initial Conditions, Final Conditions (otherwise known as Boundary Conditions), Restrictions, and so on. This and the previous step involves translating the "Word Problem" from a spoken language to the language of Mathematics so that it can be solved by precise and logical manipulation. Mistranslation is a frequent source of misunderstanding of a problem and a consequential incorrect Answer. A brief return to Steps 1 and 2 for a quick check of your understanding of the Question might be good after completing this Step. (In this Step, you will also discover the immaterial details of the Problem, such as the Color of the Hat on the Bloke who drops the Stone down the Well: There is no Kinematic Equation for Hat Color.)
4. Given what you know about the Problem right now, calculate something that you don't yet know but can be found using what you do know. It may not be the Answer the Problem is asking of you, but it will likely be a step in that Direction.
5. Review what you have accomplished so far. Return to Step 4 again, using the new Information you found from the previous application of Step 4.
6. Repeat Step 5 as many times as necessary until completion of the Problem.
7. Check your Solution. Review the whole Problem, including reading again the original Question to be sure that you haven't forgotten something or misconstrued the Facts. Check to make sure your Units are consistent. (That means, of course, writing the Units to your Answer(s) immediately after the numerical Result. This is extremely important, because a Naked Number is almost always worthless. For example, does 9.8 mean 9.8 chickens (where did the 0.2 chicken go?), 9.8 miles (km?), 9.8 gold bricks (I'd settle for the 0.2 leftover), 9.8 kg (lbs?), ...? (A mixup on units between the manufacturer and NASA is what caused the loss of a multi-billion dollar Mars probe.)
8. Review your Answer. Is it a reasonable Answer, given the Facts with which you started? For the "6 Second Deep Well" problem, does an Answer of 1.6 m seem reasonable? How about 16 m, or 1600 m? If not, recheck your calculations.
9. When you are satisfied with your Answer, indicate it as such by double-underlining it, or drawing a box around it.

Generally, perform your Calculations algebraically for as much of the problem as possible. That is, do your manipulation of the Equations in symbolic form from the start of the problem for as deep into the problem-solving procedure as you can go. Only then should you substitute numerical values. The reason for delaying numerical substitutions is so that Simplifications and Cancellations of Common Factors will occur while still in algebraic form. This will save you much Effort on the whole and will tend to reduce calculational and mathematical/logical Errors (and help you find them when they do occur).

Still having Trouble in Physics? Many students believe they are having Trouble with Physics when the real Source of their Trouble is their rusty (perhaps unused) Mathematics Skills. Since it is impossible to do Physics without Mathematics, you will need to polish up those Skills. A good place to do that is in a Physics course, but you will have to be a bit more careful for a while until you shine at it. (You can always pick up a cheap Review Book to assist you. Shaum's Outlines and other similar Books are good choices.)

Don't be afraid of making Mistakes in your Homework or Exams. Being in School is a good safe place to make Mistakes. (No Bridge will fall down as a consequence, for example.) Just make sure you learn from your Mistakes (and from those of Others). In fact, we learn more from our Mistakes than from our Successes! So when they occur, take advantage of them: You might as well, because you are stuck with them in any case.

This is a popular cartoon about Einstein, but the source of its humor is the deliberate mischaracterization of his work. He did not guess at his famous energy formula E=mc2, but went through a thorough mathematical and theoretical derivation from known facts (i.e., problem-solving) to arrive at it.

Just so you know, Einstein did have a sense of humor.

As you can see, there is little room for Guessing. The closest a Physicist or Engineer gets to guessing is Informed Estimation. That is using your Experience and Skill to assess a Situation when you have insufficient Information or Opportunity to solve a Problem correctly and completely. But the Experience can come only from complete Problem-Solving using methods similar to above.

In general, Problem-Solving involves a Multi-Step Process. Because of that, you will probably have no clue as to what the Final Answer is until you get there. Again, you'll just have to keep the Faith and practice the Patience. I have found that the source of most student's Frustration when first attempting Physics Homework is the unrealistic Expectation that the Answer to a Problem can be found in only one Step. One Step Solutions to Physics Problems are relatively rare. The same goes for Problems in the "Real World" of Checkbook Balancing, Trip Planning, House Repairs, Disputes, etc.

The Problem-Solving Skills you master during a Physics Class can easily be carried over to Problems that have nothing to do with Physics. And you should carry them over, with modifications as needed. Why? The official Label for Problem-Solving is Critical Thinking, a Life Skill everyone should master and use.

Study Location and Environment
While you are studying, do it where and when you can focus on your studying. That is, keep the Distractions to a minimum. Any Calm Place will do obviously, but a quiet spot is not required. Visual Distractions are much more disruptive of otherwise focused Attention than are Acoustic Distractions. So, the Television should be off, but the Stereo can be on. In fact, Background Music is great for studying. It accomplishes two things. It tends to induce a Calm Mind capable of intense Concentration as well as help to filter out any remaining Distractions. But the Music itself can't be distracting.

KCRB is MPR's Classical Music station in Bemidji, Minnesota.

The best music for studying is Instrumental Music in general and Classical Music in particular: Generally, it does not have a heavy beat and there are no Lyrics to intrude upon your Thoughts.

KAXE is an independent Public Radio station originating out of Grand Rapids, Minnesota.

Here in Minnesota, we have what is arguably the best network source for Classical Music in the Country: Minnesota Public Radio. It's Library of Music is among the largest in the World, which means you won't hear the same Piece twice in a Month. For those of you so unfortunate to be outside the broadcast reception area of an MPR station, their Web Site offers an audio-stream Webcast at certain times of the day. Further, I understand some Cable Systems carry MPR in addition to other Classical Music sources. A close second choice for Background Music is Instrumental Jazz. In our neighborhood, KAXE is a good source of a relatively quiet, if eclectic, mix of music if you are into late night studying. (They, too, offer audio streaming.) Of course, a good CD collection of Classical Music or Jazz will suffice, but you will not get the variety as from the Radio.

Miscellaneous Study Techniques
Take thorough Lecture Notes. They will become your Second Textbook, an Alternate Perspective from your readings of the Class Textbook. If you have the Time, Fortitude, or Stubbornness, rewriting your Notes neatly, with occasional extra stuff from the Text, will help cement the Ideas and Examples into your Brain as well as provide a coherent Review of the Topic. I personally had little time to do this as a Student, but if you do, do it on a weekly basis or so. That way, it will still be fresh in your Mind and you won't have to guess at what you wrote two months earlier. Either way, use you Notes as a detailed Crib Sheet for your last minute Study just before an Exam.

Should have asked the burning question that was on his mind way back in Surgery 101, huh?

If you don't understand something an Instructor has said during the Lecture, don't be afraid to ask for a Clarification. Don't accept a simple reiteration of the same confusing statement (confusing to you, anyway). Most good Instructors delight in Questions being asked in class, but be brief and concise. Don't drag it out. If necessary, pursue your Question after class or make an Appointment for a later time. Some Instructors may prefer this to in-class Questions, particularly for large classes, so be sure to understand his Policy on this. But the Bottom Line is, "There is no such thing as a dumb question, except for the one that is not asked." Keep in mind, though, any Question should be relevant to the topic of the day (or week).

Only the (positively) important passages are highlighted. Notice there are two levels of highlighting here, the yellow, done on the first detailed reading, and the red, on the second. Also, the typically wide outside margins give you plenty of room for notes to yourself. Click on the image for the full size version.

A lot of Students highlight or underline in their Textbooks as they read it. That's OK. I have done it, and still do. It is important to highlight the right things, however, and also, perhaps, at the right time. Highlighting on the First Pass is inappropriate certainly, and maybe even on the Second Pass. Whenever you highlight certain Sentences or Phrases (I like nonflourescent yellow myself), make sure it is a point you do understand, not a point you don't understand. Reminding yourself of your lack of understanding of something does you no good and may negatively reinforce it. Think positive. You will get it eventually, just don't highlight it until you do. Go back earlier in the same Section and reread it. Do the same with the relevant parts of your Lecture Notes. Ask a fellow Classmate. If you get really desperate, ask the Instructor. Just don't give up. If it seems like your just hitting your Head against the proverbial Brick Wall, STOP. (If you don't, you'll just get a headache.) Go do something else for a while to let your Subconscious work on it. A good way to test your Understanding of something is to try to explain it to someone else. If you have no available and willing audience, talk to yourself out loud as you explain it. The mere Verbalization of a new Concept forces you to organize your Thoughts so that your spoken words will actually help you learn it.

Priorities; Self-Discipline; Recreation
Set your Priorities as a College Student. One set of Priorities should be a listing of your most important Courses down to your least important. Your Classes in the Major should be at the top of the List. Another set of Priorities should be a No-Brainer: Your Classes come first, everything else second. (Of course, eating, sleeping (no more than eight hours), and bathing trump even your Major Classes.) If you have to, set minimum daily Study Goals that must be met before Playing. At any rate, stick to your priorities. It will be a good habit that will do you well after graduation, when you have to live in the Real World.

The proverbial Brick Wall. Bang your head against this for a while and you will indeed get a headache to remember (no memorization needed.).

There are no short cuts to Studying. Deliberately skipping Classes and not doing your Assignments create very noticeable Effects that your Instructors easily see. You can not cover up these Effects by asking Questions in and out of class, or by repeating memorized Phrases on an Exam. Your Instructors are interested in how you arrived at your Answers more than the Answers themselves. It is the appropriate Reasoning, the Problem-Solving Skills, that you display to your Instructors and will eventually master that will make you a valuable Professional Physicist, Engineer, or Mathematician upon Graduation. And it requires lots of Studying and Practice to get to that point.

After you have established a set of good Study Habits and start to experience the benefits, you will begin to understand the statement "Talent alone won't get you where you want to professionally go nearly as well as Self-Discipline" (that is, the Discipline of good habits that you impose upon yourself). History is full of individuals who were smart and talented, and had the Opportunities to take advantage of their Intelligence and Skill, but failed to accomplish anything. They failed because they lacked the Self-Discipline required to develop their Talent and maintain the Patience to constructively use it. With respect to studying for your classes, I will go so far as to say "Self-Discipline is so much more important that it can make up for any lack of Talent you believe you have!"

A four-way balance. Hard Work must be balanced by Hard Play while High Intellectual Thought needs to be balanced by Intellectually Simple Play.

One more Caveat: Don't forget to have some Fun. You'll need it to keep your Life in Balance, especially if you devote a lot of Time and Effort to your Studies. There are two Canons that apply. The harder you work (that is, study), the harder you must play, and The more intellectual your Work, the simpler should be your Play. Just make sure your Play doesn't get in the way of your Studies, and generally don't let it be on-the-spur-of-the-moment.

Mr. Spock when he was a mere Lieutenant Commander in the original 1960's Star Trek television series.

Now I can answer the "complaints" mentioned earlier about getting As and Bs in other classes but not in these Science classes that seem so much more difficult. Studying the Sciences requires more than mere Scholarship. It also requires knowledge of the (scientifically established) Facts, how they are discovered, and how they uniquely fit together to create a Big Picture that may well be at odds with prior established conclusions. Although there is a lot of Creativity involved, the great bulk of the effort in Science is arriving at logical, self-consistent, and universal Understandings that include all the Facts. Academic study outside the Sciences and Mathematics does not always require this level of carefulness and universality, although it can (and frequently does). Simply said, you cannot bullshit your way through Science: Faulty or incomplete "facts" or Assumptions, even if subsequently coupled with perfect Logic and Scholarship, are worthless in Science. (Captain Spock said it best in Star Trek VI: The Undiscovered Country: "Logic is only the beginning of wisdom, not the end.") Guessing doesn't work either. Studying Science requires the same quality of effort as doing Science. Hence, what might have worked before in a non-Science class won't work now in a Science class. And because of the extra effort needed to achieve the same academic grades, Science classes ARE more difficult.

But it isn't all that bad. Why? In my opinion, I have yet to meet a college student who is incapable of achieving an A+ in a Physics class (presuming, of course, that all prerequisites and High School Graduation Requirements were met prior to the class in question). The only reasons a student does not so reach the A+ are Bad Study Habits, Lack of Interest, or Lack of Time. These reasons have nothing to do with Intellectual Capacity, however. So never think of yourself as not being smart enough to do Physics. Rather, at worst, view yourself as someone with Interests that lie elsewhere.

Conclusion
If you follow the Ideas presented here, and get into the habit of putting in sufficient amounts of Quality Studying, you will eventually discover its Dividends are priceless. The Dividends will include Efficiency of Understanding and Skill, an Automatic View of the Big Picture simultaneous to Attention to Detail and the Relationship between them, and a reputation for being Reliable and Productive.

More Stuff
For other sources for Study Hints, use Google or some other Search Engine using combinations of the keywords study, study hints, physics, engineering, and mathematics. A very good article on how to study Physics, although a bit dated (and sans pictures), was written more than 50 years ago by Seville Chapman. Donald Simanek of Lock Haven University has created a slightly edited pdf version of it. Chapman's article "How to Study Physics" is available here. Another good article on how to study Physics that is a bit more recent (1977, revised 1997) is by David R. Hubin and Charles Riddell at the University of Texas at Austin. Hubin's and Riddell's article (revised by Lawrence C. Shepley) "How to Study Physics" is here.

I won't wish you Good Luck because you already have it. Luck favors the Prepared.

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Last updated October 3, 2009
2009 Stevens F. Johnson and the Dept. of Physics/Science, Bemidji State University. All rights are reserved unless explicitly stated otherwise.
Thanks to the anonymous contributors of most of the figures and pictures. Your contribution to the academic health of those who have read this article is greatly appreciated.