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Every time I start a hard problem and if can not figure out the exact solution or can not get started, I get into this never ending discussion with myself, as below:
That problem
solving/mathematics/algorithms skills
are gifted (not that you can learn
by practicing, by practice, you only
master the kind of problems that you
already have solved before)
only those who went to good schools can do it, as they learned it early.
What are your thoughts, can one achieve awesomeness in problem solving/algorithms just by hard work or you need to have that extra-gene in you?
I spent a big part of my life wondering whether talent was something you developed or something you were born with. Then it occurred to me that the answer was irrelevant, at least if you want to achieve things yourself. Even if you have talent, it will only help you if you act as if talent only comes from practice, because you will work that much harder.
With regards to algorithms, as well as any other really difficult skill, it takes practice to get good. Whether or not you have to have some amount of talent too, I don't know. I do know for a fact, however, that people have made huge improvements in competitions like TopCoder by practicing. I myself have learned a lot from that.
If you set up a systematic training program, you will be way ahead of the pack, even if it is not perfect. I have written a few hundred programs on TopCoder by now and it has affected my thinking in a profound way. I have learned a lot of things that could only ever be learned by doing them wrong and then fixing my mistake. A friend of mine has written several thousand programs on TopCoder and he is way better than I am, even though his stats were worse when he started out than mine were. That is no coincidence.
EDIT:
I just came across this answer at math.stackexchange. I think it is one of the best explanations of how to learn algorithms I have read, even though he writes about chess and math.
1) Don't try to solve the problem in its most general abstraction.
2) Choose the right time when your mind is working at maximum.
I got the first point as an advice from a math instructor. It works! try to do different examples and scenarios of the problem. This helps greatly in identifying the edge cases which are the hardest to understand in most problems.
My favorite time for solving this kind of problems is the dawn(4-6 AM). Have a good sleep the night before, and wakeup ready to solve the problem. Silence is your friend.
I do believe that some people have extra intelligence than others, but it is not the most important factor. It is how you utilize this intelligence to solve the problem.
I took magic lessons in a group setting when I was twelve years old. The magician's name was Joe Carota. He did a magic trick one time and I blurted out, "How did you do that?" He said something that day that has stuck with me ever since.
Joe's response, "Michael, if you really want to know how that trick is done you must figure out how you would do it yourself."
Well of course that's not what I wanted to hear but it did get my mind focused on problem solving. This was problem solving from my perspective. If my first attempt at solving the problem took seventeen steps and was really klunky, the good news was I solved the problem.
Then by looking at the solution I had developed and further looking for ways to refine that solution I would learn how to streamline the end result. Later on in my computer programming life I found out that this process was called "Stepwise Refinement".
It worked back in 1971 and it still works today.
For me, i think it's a bit talent, but much more important is experience and practice. If you know many problems and the best solutions to them, you can come up more easily with a solution to a new problem.
Example from my own past: There was some programming contest (good for training, btw) and I did not find a good solution. The winner solved the problem mainly by using a KD-Tree. To come up with this, you first of all need to know what, in this case, a KD-Tree is, and where it's useful. Today, this is clear to me and if i'd encounter a similar problem again, i'd be able to solve it really quickly.
Hardwork beats talent if talent doesn't work hard.
This above statement defines what the true potential of persistence is.Any skill in this world can be developed by practice.This process is analogous to nailing a nail in the wall.It not only requires correct magnitude but also appropriate direction.
To answer the question, first we need to find the ingredients for the capability to solve an issue.
There is a so-called natural talent. This is the talent you are born with. This predetermines your potential. People born with more gray matter will tend to perform better than people with whom nature was less generous with. This means that a person having better talent has a higher probability to perform better than a person not as talented if they had the same parameters (education, personality, resistance to stress, willpower). If one observes that he or she tends to consume a great time to absorb new information until he or she is able to apply it, then the wisest decision for the person is to leave programming and prevent a life full of frustration. Naturally, one cannot expect as a beginner to be able to instantly understand the most complex phenomenon, but if a beginner is too slow to understand beginner concepts, then programming is not his or her cup of tea.
Developed talent. One has a natural talent, but that is, in itself not enough to solve problems. I have never seen newborns writing code. One has to get some education. The earlier, the better. Also, the quality of school is of high importance. We should never deny the fact that a person who did not have the chance to learn programming at a good school early, then he or she has a handicap in the race for success. However, if someone misses good schools early, then the handicap can be covered with hard work. For instance, my wife had an education in another field, but after finishing the university, she did not find proper jobs. So I started to educate her. After a month she learned how to learn and was able to solve almost any problems presented to her, but she was not yet effective. She gradually became to start learning in auto-didacting manner. After a year she was already a professional coder. She does not have a paper from a school that she can code, but she is doing a fantastic job. So, she missed early education, but was later able to neutralize the handicap. Developed talent can be described as the set of information learned and known, along with the right attitude, the scientific approach to new types of challenges.
Practice: Practice is good to increase the level of developed talent, yet, it SHOULD not be the sole source of developing talent. Along with practice, the theoretical horizons must be regularly expanded.
Working strategy: One can be extremely talented, can have a lot of knowledge. If he or she does not have a right working strategy, then he or she has a handicap. Whenever a new task is given, the right questions should be asked:
what was the closest task to this one? Can I reuse my solution to an extent?
what should I learn to be able to solve this problem?
how can I write clear and efficient code to solve the problem?
So the answer is: while it is good to have excellent education as early as possible, it is not necessary. Do not forget, that life is the best school and you can recuperate the lost opportunity later if you have talent, willpower and source of information. Practice is not only showing you the right steps to solve a problem, it also widens your horizons. For instance, if one understands number systems, then he or she will be able to understand a variety of things later, like colors in CSS, PSD, or number overflows. If one learns how to code in Java, then he or she will understand C# very quickly. So, practice is giving you knowledge about the solution to a given problem type, but also, gives new theoretical knowledge which will be useful in various areas. The core skill one has to develop is the ability to learn quickly.
There have been many examples of people having extraordinary talent with minimum success. You see such examples in sports,politics,business and also in general around you. So, I feel after a certain limit, talent is a meaningless virtue. Its mostly the hard word that rewards you with greater success. If you follow cricket, here is a link with good example.
I feel same principle applies to algorithm and problem solving. An year back I use to pick up algorithmic problems to solve and used to find myself completely lost. An year invested in reading algorithmic books, solving its exercises and also practicing some more programming problems, I am confident that now I can solve most problems ( I still have a long way to go in making myself efficient in it). But the point is smart work is enough to develop this knack of solving problems.
Talent is cheap and useless without hardwork. Talent can only take you to some extent, but with hardwork and practice anybody can reach great heights
- Josh Waitzkin, 8-time National Chess Champion, a 13-Time National and 2-time World Champion
He himself says this in his voice over in Chessmaster Grandmaster Edition
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I've taken everything up to pre-calculus in college, but when trying to get through things like the Donald Knuth books, or even things like this link: http://en.wikipedia.org/wiki/Self-balancing_binary_search_tree I wind up looking at math that means absolutely nothing to me. I'm not looking for magic, I don't expect to make sense of this in a week, I'm just looking for a good graduated plan of things to read / explore to get me there. Any pointers are welcome, after 20+ years as a professional programmer, I feel it would be nice to have this under my belt. Thanks in advance to everyone! :-)
I actually recommend taking a discrete mathematics course at your local university. This helped me out tremendously. Until I had this, I did not understand recursion (which is based on mathematical induction.) There are a number of other concepts which you will learn in a good discrete mathematics course which are extremely, extremely helpful (graph theory, asymptotic notation, combinatorics...)
I also recommend taking the class for a grade. I have always noticed that this makes people take the course more seriously, even if it is not in line with a degree path or anything past the grade.
If your local university is good, they will likely have tutoring sessions and office hours available that you can go to in order to ask questions and get clarification. These are really, really valuable and helped me learn things in a deeper manner, and more quickly, than I ever could have on my own.
You may need to take calculus in order to meet the prerequisites, but that is something I would also recommend if you'd like to increase your mathematical literacy. This 'answer' will take at least a semester, and more like two, but I think this is the way to go. It's not an immediate solution, but you will become better at math if you perform well in these two classes (and you have a good university close by.)
Your profile says you are in Dallas. I found this course (with no prerequisites!) for you. The syllabus looks like it covered a lot of good material, and the course met at 5:30 p.m. (good for working people!). If they are offering anything similar next semester, I'd consider it. If you call up the instructor, I'm sure he'd be happy to talk with you about what he knows for summer and fall scheduling.
This path has worked well for me.
Good luck!
You can try this: http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025
There's a pdf version of this available online, you can easily google it out.
Many of my friends who are great programmers recommended it.
A lot of talented programmers understand algorithms before understanding the maths behind them. Maths are only there to help, they are not here to make you understand everything. You will need to spend more time reading about algorithms and complexity, then you might get a sense of how to evaluate them.
I recommend you to read more books about algorithm complexities.
In your long experience as a professional programmer, there surely are topics and sub-domains that you are most curious about. My advice is: identify those areas and go after them. It might be code-breaking, number theory, recursion, functional programming, computational origami, logical puzzles, crystal structures, graphs, genetic algorithms, splines...
Take your own remark to heart:
but when trying to get through things like the Donald Knuth books, or even
things like this link:...I wind up looking at math that means
absolutely nothing to me
What sort of math fascinates you?
I could say there are lots of intriguing puzzles at Project Euler. After you solve a programming challenge, you have access to a forum in which other folks share their solutions and occasionally refer to some body of knowledge they were drawing on. I love it. But what matters is what you like. Your own interests are the key to your learning.
If math and programming no longer have any appeal--you don't like doing them in your spare time--find something else to get into: acting, foreign languages, travel, French cooking, biking. Who knows, maybe you're burned out.
I'd say get a good book in discrete math and one in combinatorics as well. Here are a few I've liked. The Rosen book is good place to start.
http://www.amazon.com/Course-Combinatorics-J-van-Lint/dp/0521006015
http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073229725/ref=sr_1_2?s=books&ie=UTF8&qid=1305304408&sr=1-2
http://www.amazon.com/Introductory-Combinatorics-5th-Richard-Brualdi/dp/0136020402/ref=sr_1_7?s=books&ie=UTF8&qid=1305304434&sr=1-7
In line with what Vincent said, I recommend Algorithms in a Nutshell from O'Reilly (here).
There is a plenty of good video-lectures on Discrete Math, Calculus and Applied Math. Just watch them every evening, make notes and try to solve simple problems. To prepare yourself for Knuth, try "Discrete Mathematics". To understand deeply what is math and how all things in the universe are interconnected (including algorithms), try "Joy of Mathematics".
I was looking for just the same thing. I couldn't afford any of the material suggested here so far so here's a link to a YouTube lecture series on Discrete Mathematics. I wish there was a playlist but unfortunately there is not.
The videos are taken uploaded from http://www.aduni.org who ask for a donation of 25c per video to cover operation costs.
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Is it important for developers to know discrete math? Most of the books about algorithms and analysis have at least some references to math. I can easily understand the algorithms in principle and can implement them without any problem, but when it comes to the math parts I get stuck. Is it generally assumed that developers will have deep knowledge of math to understand algorithms and methods?
It depends on the kind of developer you're talking about and the kind of math you're talking about. I'm pretty sure that most of the "ordinary" developers don't need to know much about math. But, do you want to be "ordinary" developer?
If you're developing web applications that just display and allow editing of data in database, then you'll probably never need any math.
On the other hand, if you're developing a GPS system that shows a path to the target (or some other application that does more complicated calculations) then discrete math is going to be useful.
It doesn't necessarily be discrete math though - for example, in the finance industry, people need probability and statistics far more often.
That said, knowing math will definitely make you a better developer, because it trains your mind in a way that is useful not only for solving specific (math) problems, but also teaches you how to think about problems in a more formal fashion (which, I believe, is important for writing correct code).
Yes.
I find that discrete math is fairly core to computer science. Understanding set theory, boolean algebra, maps, etc. are all beneficial to a developer and are all part of discrete math.
Of course, the concepts won't always be applicable in the most academic sense. You will almost never open your discrete math textbook and copy something into your code to solve a problem. However, understanding those concepts will help developers write better code, better algorithms, and use design patterns more effectively.
Depends on what the developer is doing probably. If you are doing web, probably not, maybe a bit when it gets to security. Like the time a brute force attack takes to decode a key of certain number of bit under a certain hash. If you are doing graphics for high end games, you probably need to understand quite a bit of maths and the pros and cons of the methods. As a DB admin or network, you shouldn't.
The kinds of problems that you get the chance to solve depends on what you know.
If you only know 4th grade math, you'll only be asked to solve problems that involve math that's at a 4th grade level or less.
If you aspire to do more or understand the underpinnings of other algorithms, you'll have to learn whatever math is necessary.
I think you'll find that working through the points where you get stuck will improve your math, your appreciation for the problems you solve, and a better chance at extending the math you learn to new areas.
It nauseates me to hear people immediately disparage an area that they find difficult, as if to justify their unwillingness to push past the pain of ignorance and struggle. Learning any new skill requires that you push through that barrier, be it math or anything else. I'd advise you to stay with it and prove to yourself that you can master something difficult by resisting the urge to give up.
You have already found out that the results of discrete mathematics are useful in programming. My experience is that understanding why something works, rather than attempting to simply follow it by rote, allows you to find and fix many errors and misunderstandings. It also allows you to handle situations that are almost, but not quite, the way they are in the textbook, and to realise when the textbook answer no longer applies. Time spent understanding even a small part of something that you might use or work on will not be wasted.
If your job is pure CS like Google search where you invent new algorithms then yes, you'll need to be able to analyse running times quite well, also anything sciency like physics simulations.
If you're a 'normal' developer then you'll need to know about running times and what they mean and their impact on your application.
My experience is this:
Knowing something about discrete mathematics is something you will never regret. It will make your job easier in many instances, even in mundane tasks, because you will be familiar enough with various concepts that will at least allow you to construct a smarter google query. In depth familiarity and ability to do these things by rote is probably not helpful to most programmers, but a passing familiarity definitely is.
That said, most programmers in industry that I've encountered (and even some in academia!) know almost nothing about this stuff, so not knowing it is unlikely to place you at a significant disadvantage outside of a few specialist programming sub-disciplines.
You're generally not expected to have a deep knowledge of maths, unless the application requires it - e.g. you're writing financial software, or doing some 3D modelling, load balancing on aircraft, writing some tailored compression algorithm etc. I've worked with great developers who struggled with simple maths. And knowing discreet maths seems very specific. Having an understanding of how a variety of algorithms work can be helpful, and if you can do that it doesn't much matter that you can't construct a proof of their optimality etc.
To be honest what I think is most important is understanding the business you're building for, and how you approach writing code (readability, modular etc)
Some knowledge of discrete math might someday help you stop before spending a lot of time attempting to code up something mathematically impossible or of NP complexity to solve. You will gain a much better "feel" for when some proposed software problem or solution path more resembles an easy homework assignment, or one of those term projects which no one in your class ever completed.
It depends about what part of discrete math you are talking. Of course knowing math will always be an advantage... but I think that knowing of some parts of discrete math are not just advantage, but are very essential for a developer (of course it depends from projects on which he/she is working).
But topics like :
Set theory
Graph theory
Alg. Analysis
Alg. Complexity
Sorting
etc...
are essential for a developer.
at workplace, the work I do is hardly near to challenging and doing that I think I might be losing the skills to look at a completely new problem and think about different ideas to solve it.
A friend suggested TopCoder.com to me, but looking at the overwhelming number of problems I can not decide how to get started?
what I want is to sharpen my techniques ( not particular language or framework ).
The only way to get started would be to pick problems. Division I is the more difficult division, so you will probably find that the division I medium and hard problems will be somewhat interesting and challenging (unless you are quite clever.)
If you check the event calendar, you can see what algorithm competition rounds are coming up in your time zone. The competitions have the added virtue of forcing you to read and analyze other people's code in the challenge phase, so even if you would just as soon practice without a clock, you may find them interesting.
TopCoder algorithm contests are a way to develop your coding speed. Solving any of the problems in the practice arena is difficult unless you already have knowledge of various algorithms.
The problems on Project Euler suffer from the same flaw. You already have to know the algorithms to solve the problems in a reasonable time frame.
What I would suggest is to pick a project that you're interested in, and pursue it as you have time. As an example, I'm currently learning how to work with the open street map tiles in an Eclipse rich client platform.
Try whit http://projecteuler.net Problems difficulty can be assumed by number of solvers.
I prefer this page, because it is language invariant and problems are really challenging
You need the experience of solving 2 problems in any online judge (like http://www.spoj.com, http://www.lightoj.com, http://www.codeforces.com) in any programming language of your choice. That will give you an idea about how are your programs tested online.
Then you can follow this -> http://localboyfrommadurai.blogspot.in/2011/12/new-to-topcoder.html
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I was thinking about ways to improve my ability to find algorithmic solutions to a problem.I have thought of solving math problems from various math sectors such as discrete mathematics or linear algebra.After "googling" a bit I have read an article that claimed the need of learning game programming in order to achieve this and it seems logical to me.
Do you have/had the same concerns as me or do you have any ideas on this?I am looking forward to hear them.
Thank you all, in advance.
P.S.1:I want to say that I already know about programming and how to program(although I am at amateur level:-) ) and I just want to improve at the specific issue, NOT to start learning it
P.S.2:I think that its a useful topic for future reference so I checked the community wiki box.
Solve problems on a daily basis. Watch traffic lights and ask yourself, "How can these be synced to optimize the flow of traffic? Or to optimize the flow of pedestrians? What is the best solution for both?". Look at elevators and ask yourself "Why should these elevators use different rules than the elevators in that other building I visited yesterday? How is it actually implemented? How can it be improved?".
Try to see a problem everywhere, even if it is solved already. Reflect on the solution. Ask yourself why your own superior solution probably isn't as good as the one you can see - what are you missing?
And so on. Every day. All of the time.
The idea is that almost everything can be viewed as an algorithm (a goal that has some kind of meaning to somebody, and a method with which to achieve it). Try to have that in mind next time you watch a gameshow on TV, or when you read the news coverage of the latest bank robbery. Ask yourself "What is the goal?", "Whose goal is it?" and "What is the method?".
It can easily be mistaken for critical thinking but is more about questioning your own solutions, rather than the solutions you try to understand and improve.
First of all, and most important: practice. Think of solutions to everything everytime. It doesn't have to be on your computer, programming. All algorithms will do great. Like this: when you used to trade cards, how did you compare your deck and your friend's to determine the best way for both of you to trade? How can you define how many trades can you do to do the maximum and yet don't get any repeated card?
Use problem databases and online judges like this site, http://uva.onlinejudge.org/index.php, that has hundreds of problems concerning general algorithms. And you don't need to be an expert programmer at all to solve any of them. What you need is a good ability with logic and math. There, you can find problems from the simplest ones to the most challenging. Most of them come from Programming Marathons.
You can, then, implement them in C, C++, Java or Pascal and submit them to the online judge. If you have a good algorithm, it will be accepted. Else, the judge will say your algorithm gave the wrong answer to the problem, or it took too long to solve.
Reading about algorithms helps, but don't waste too much time on it... Reading won't help as much as trying to solve the problems by yourself. Maybe you can read the problem, try to figure out a solution for yourself, compare with the solution proposed by the source and see what you missed. Don't try to memorize them. If you have the concept well learned, you can implement it anywhere. Understanding is the hardest part for most of them.
Polya's "How To Solve It" is a great book for thinking about how to solve mathematical problems and do proofs, and I'd recommend it for anyone who does problem solving.
But! It doesn't really address the excitement that happens when the real world provides input to your system, via channel noise, user wackiness, other programs grabbing resources, etc. For that it is worth looking at algorithms that get applied to real-world input (obligatory and deserved nod to Knuth's collection), and systems which are fairly robust in the face of same (TCP, kernel internals). Part of coming up with good algorithmic solutions is to know what already exists.
And alongside reading all that, of course practice practice practice.
You should check out Mathematics and Plausible Reasoning by G. Polya. It is a rare math book, which actually deals with the thought process involved in making mathematical discoveries. I think it is the same thought process that is involved in coming up with algorithms.
The saying "practice makes perfect" definitely applies. I'm tutoring a friend of mine in programming, and I remind him that "if you don't know how to ride a bike, you could read every book about it but it doesn't mean you'll be better than Lance Armstrong tomorrow - you have to practice".
In your case, how about trying the problems in Project Euler? http://projecteuler.net
There are a ton of problems there, and for each one you could practice at developing an algorithm. Once you get a good-enough implementation, you can access other people's solutions (for a particular problem) and see how others have done it. Don't think of it as math problems, but rather as problems in creating algorithms for solving math problems.
In university, I actually took a class in algorithm design and analysis, and there is definitely a lot of theory behind it. You may hear people talking about "big-O" complexity and stuff like that - there are quite a lot of different properties about algorithms themselves which can lead to greater understanding of what constitutes a "good" algorithm. You can study quite a bit in this regard as well for the long-term.
Check some online judges, TopCoder (algorithm tutorials). Take some algorithms book (CLRS, Skiena) and do harder exercises. Practice much.
I would suggest this path for you :
1.First learn elementary parts of a language.
2.Then learn about some basic maths.
3.Move to topcoder div2 easy problems.Usually if you cannot score 250 pts. in any given day,then it means you need a lot of practise,keep practising.
4.Now's the time to learn some tools of a programmer,take a good book like Algorithm Design Manual by Steven Skienna and learn about dynamic programming and greedy approach.
5.Now move to marathons,don't be discouraged if you cannot solve it quickly.Improvement will not happen overnight,you will have to patiently keep on working hard.
6.Continue step 5 from now on and you will be a better programmer.
Learning about game programming will probably lead you to good algorithms for game programming, but not necessarily to better algorithms in general.
It's a good start, but I think that the best way to learn and apply algorithmic knowledge is
Learn about good algorithms that currently exist for your area of interest
Expand your knowledge by viewing other areas; for example, what kinds of algorithms are
required when working on genetic analysis? What's the best approach for determining
run-off potential as it relates to flooding?
Read about problems in other domains and attempt to use the algorithms that you're
familiar with to see if they fit. If they don't try to break the problem down and see if
you can come up with your own algorithm.
A few more books worth reading (in no particular order):
Aha! Insight (Martin Gardner)
Any of the Programming Pearls books (Jon Bentley)
Concrete Mathematics (Graham, Knuth, and Patashnik)
A Mathematical Theory of Communication (Claude Shannon)
Of course, most of those are just samples -- other books and papers by the same authors are usually quite good as well (e.g. Shannon wrote a lot that's well worth reading, and far too few people give it the attention it deserves).
Read SICP / Structure and Interpretation of Computer Programs and work all the problems; then read The Art of Computer Programming (all volumes), working all the exercises as you go; then work through all the problems at Project Euler.
If you aren't damned good at algorithms after that, there is probably no hope for you. LOL!
P.S. SICP is available freely online, but you have to buy AoCP (get the international, not-for-release-in-north-america edition used for 30 USD). And I haven't done this yet myself (I'm trying when I have free time).
I can recommend the book "Introductory Logic and Sets for Computer Scientists" by Nimal Nissanke (Addison Wesley). The focus is on set theory, predicate logic etc. Basically the maths of solving problems in code if you will. Good stuff and not too difficult to work through.
Good luck...Kevin
Great
how about trying the problems in Project Euler? http://projecteuler.net
There are a ton of problems there, and for each one you could practice at developing an algorithm. Once you get a good-enough implementation, you can access other people's solutions (for a particular problem) and see how others have done it. Don't think of it as math problems, but rather as problems in creating algorithms for solving math problems
Ok, so to sum up the suggestions:
The most effective way to improve this ability is to solve problem as frequently as possible.Either real world problems(such as the elevators "algorithm" which is already suggested) or exercises from books like CLRS(great, I already own it :-)).But I didn't see comments about maths and I don't know what to suppose(if you agree or not).:-s
The links were great.I will definitely use them.I also think that it will be a good exercise to solve problems from national/international informatics contests or to read the way a mathematician proves a theorem.
Thank you all again.Feel free to suggest more, although I am already satisfied with the solutions mentioned.
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Our profession often requires deep learning; sitting down and reading, and understanding. I'm currently undergoing an exam period, and I'm looking for ways to learn more effectively.
I'm not asking about what to learn, or whether to prefer blogs over books, etc. My question is much more physical than that -
What do you do when need to study, and I mean study hard?
I'm looking for answers such as
I slice my time to 2.5 hours intervals and make a break between them, but never during.
I keep a jar of water nearby.
I wake up at 6 o'clock sharp and start my day with a session at the gym.
What good learning habits did acquire, or wish you had acquired?
(I know this isn't strictly programming related, but it is programmers related)
I find the best way to set yourself up for learning is:
Get plenty of exercise and rest
Eat a balanced diet with little sugar and caffeine
Try to find a quiet area conducive to concentration
Try to practice what you learn from a book - theory is ok, but practice embeds the knowledge.
"The best way to test whether or not you know something is to try to explain it to someone else from scratch."
That has to be one of the best ideas I was ever given about knowing whether or not I really know something.
Make sure it's quiet and comfortable around you.
enough to drink and eat
don't just read but take notes, draw mindmaps and the like
don't just read but try
make a report, blog entry, presentation out of what you learned
learn the same thing from different sources: Don't just believe what person A has to say look for, read and understand the opinion of person B and C as well and understand the differences.
take nothing for granted
apply the knowledge to an actual project
I set aside time every day or x times per week. Otherwise I never do it.
I try to have a diff location every once and awhile (home / coffee shop / stay late at the office) keeps the tedium away.
I am careful about the music I use, try to make sure it is relaxing
Sometimes I leave headphones on even if music is off that way people don't talk to me.
I give myself specific goals before each break or for every session.
I reward myself
Read Andy Hunt's "Pragmatic Thinking and Learning" - lots of good suggestions there.
Tony Buzan wrote The Mind Map Book, describing his ideas for note taking. He also has some process ideas that I found very helpful. Foremost was this one: study new material for an hour, then take a short break (5-10 minutes) and then review the new material. Review the new material again an hour later, then two hours after that, then the next day. You need to refresh your exposure to the material multiple times over the course of time to really take it in.
While reading, I make sure I fully comprehend each section in the text before I continue.
Set up a time and take away all distractions. At home/dorm can be rough, so I would use the library while in college. Getting started is usually the hardest part, so don't set a specific time limit for when to quit. It is distracting, and you will be looking at your clock to see "how much longer you have." You don't want to be in that mindset. Work until you feel your brain is starting to lose focus, whether that is lack of comprehension or having to reread simple paragraphs repeatedly. Take a minute or two as a break, then refocus your mind. When that stops working, it is time for a real break.
Are you a night owl or early bird? Each person is different. I am very productive early in the morning, while my wife can barely function. We all have differences, so don't try to fight your nature.
+1 to what everyone else said. Making cheat sheet/notes were a very important part of my studying habits, whether I could use them on the exam or not.
I find it best to be fully dedicated to the task before I start. If you go into something with low morale, you will not do well. If you go into a task with high morale, you will understand things quicker, be able to apply it to real situations better, and will have a deeper comprehension. If I am not fully dedicated, I don't even bother. I've got better things to do with my time then half ass something, and you probably do too.
Expanding on a comment I left, see this article from Electronic Design from a few years ago: http://electronicdesign.com/Articles/Index.cfm?AD=1&ArticleID=5859.
If you can teach what you learned, you know it.
by Louis Frenzel
All learning is self-learning. Professors, trainers, and all teachers just organize and present the material to be learned. They don't teach it to you. You learn it. You're the one who actually absorbs, understands, and assimilates the knowledge by listening to the lectures, reading, thinking, solving problems, and other activities. Self-learning is a natural, human quality. While most of you have used this method in the past, you may want to do it on a more formal basis to speed up and fine-tune your methods. Here's a suggested approach (and trust me on this, you must write it down):
Clearly identify what you want to learn. Write it out.
Write some learning objectives for yourself. These statements clearly identify what you want to know and be able to do. For example, you should write something like "When I complete this learning assignment, I will be able to design and program an FIR DSP filter." The objectives should be expressed in "behavioral" terms, that is, using words that state some measurable outcome.
Identify some initial resources. Start with books at the local bookstore or go to www.Amazon.com or Barnes & Noble at www.barnesandnoble.com. Most cities don't have good technical bookstores, and it's tough to find anything at regular bookstores. Consider yourself lucky if you have a good technical bookstore or a good college bookstore. Plan to get multiple books to give you greater breadth of coverage with multiple explanations, examples, and perspectives. Don't forget to look through your stack of magazine back issues.
Check out online sources. Do one or more Web searches, or go to relevant company Web sites. You may run across an appropriate tutorial, white paper, or application note that will give you what you need. The large semiconductor and equipment manufacturers have tons of stuff on their Web sites, so start digging. Also check out the professional societies and other sources listed in the tables and sidebars.
Watch out for any conferences or seminars on this topic. Usually, such events never occur when you need them, but you might get lucky. If you find one, attend because it will provide a big head start for your own learning.
Organize your materials. Lay them out, mark them up, and then make an outline based on your objectives. See what you have and what you lack, and make an initial list of things to do.
Dig in. Set aside an hour a day or whatever you can to go through the materials. Turn off the radio, CD player, and television. Make a habit of finding some quiet time to read and learn.
Look for a human tutor. You could be working just down the hall from an expert on the very subject you're trying to learn. Pick his or her brain. Ask this person if he/she will help you understand and learn. Take this person to lunch or offer to pay for lessons. Most people will gladly share what they know, if you aren't too proud to ask. The best way to do this is to learn as much as you can on your own. Then, go for the professional, personal help with tough questions or when you get stuck.
Include some hands-on. Is there any hardware you can buy or put together to help you learn it? Maybe there's some software that will help. Buy it or have your employer buy it.
Write a paper or article or teach what you have learned. You have to know it to write it or teach it. There's no better way to learn for yourself than to have to explain it to others.
I generally find it useful to build a "cheat sheet" or other form of summary as I go.
On one hand, it forces me to reinterpret information and figure out what's really important.
On the other hand, I'm building a useful study tool for last-minute revisions, or future refreshing of knowledge.
2.5 hours without breaks seems like a lot. Experiment with different time slots to see what works best (personally, a sequence of 3x(20 work - 5 break) works well)
Pomodoro Technique for time management
http://pomodorotechnique.com/get-started/
(watch "how" tab)
And the code(for programmers)
while(day) {
for (int i = 0; i < 4; i++) {
work(25);
relax(i < 3 ? 5 : 15);
}
}
You should implement methods
void work(int minutes);
void relax(int minutes);
Variable day changes from other threads