What can you do just one thing each day to get better at logical thinking and math skills?

Yes actually, get a math book at a level you’re comfortable(better if you’re just familiar and not yet comfortable), read the first chapter and attempt some problems. It’s very important to try the problems, reading math doesn’t get you anywhere. After you’ve struggled a while(say 2 hours), if you still don’t know the answer wait a day try again for 15 min, if you still don’t get it let yourself look up the answer. It’s important not to feel guilty about looking up answers, this stuff is complicated and it has been developed for centuries, you won’t come up with anything new until after years

Yes actually, get a math book at a level you’re comfortable(better if you’re just familiar and not yet comfortable), read the first chapter and attempt some problems. It’s very important to try the problems, reading math doesn’t get you anywhere. After you’ve struggled a while(say 2 hours), if you still don’t know the answer wait a day try again for 15 min, if you still don’t get it let yourself look up the answer. It’s important not to feel guilty about looking up answers, this stuff is complicated and it has been developed for centuries, you won’t come up with anything new until after years of study. But it’s also important that you really try, because otherwise you’ll think everything is trivial when almost nothing is.

For maths skills, study maths by learning parts that are new to you. For logical thinking, try philosophy. Look for people who are saying things that may either be incorrect or counterintuitive and then try to prove which of those applies. The more thinking you do of that kind, the better, but the problem is knowing whether your analysis is right, and different people will award you different marks for it, with some people telling you you’re right when you’re wrong. That the big problem with trying to learn to think more logically because you don’t know who to believe when it comes to measurin

For maths skills, study maths by learning parts that are new to you. For logical thinking, try philosophy. Look for people who are saying things that may either be incorrect or counterintuitive and then try to prove which of those applies. The more thinking you do of that kind, the better, but the problem is knowing whether your analysis is right, and different people will award you different marks for it, with some people telling you you’re right when you’re wrong. That the big problem with trying to learn to think more logically because you don’t know who to believe when it comes to measuring how well you’re doing. That situation will only be resolved when we have AGI running on your computer and it can tell you exactly what you’re getting right or wrong.

Solve one math problem every day.

Change the areas of mathematics from where the problems come regularly.

(obviously, you can’t just go and solve a math problem from a textbook or a student homework sheet (to find on the internet) unless you have some background in the corresponding area. Establishing the background is a self-explanatory part of the understanding of and of solving the problem.)

To keep it real: at least work a couple of hours a day on such a problem. Solving often requires not just a couple of hours if the problem is hard.

I imagine there are many and a variety of “just one thing” to do each day to better you thinking and math skills. Then again, it may likely take you a long, long time to reach your expected and/or desired level of comprehension and expertise.

Spend 30–40 min learning from UNIZOR.COM. It provides video-recorded lectures with detail notes on Math and Physics. The site is totally free, no ads, no strings attached. But you need a discipline to listen to one or two lectures a day, starting from the very beginning.

Logical thinking and problem solving skills, contrary to much public opinion and even college classes, etc. has nothing to do with how much knowledge or information is in your head it also isn’t just a trick in the way you think… it takes serious wisdom and understanding the big-picture about how things work, in reality, generally and specifically. You can’t ever get that from anyone else. The best teachers are people who guide you to discover truth. Actual teaching is becoming extinct in our society. Our schools, k-12 and even colleges are filled with “tellers” and very few actual “teachers”

Logical thinking and problem solving skills, contrary to much public opinion and even college classes, etc. has nothing to do with how much knowledge or information is in your head it also isn’t just a trick in the way you think… it takes serious wisdom and understanding the big-picture about how things work, in reality, generally and specifically. You can’t ever get that from anyone else. The best teachers are people who guide you to discover truth. Actual teaching is becoming extinct in our society. Our schools, k-12 and even colleges are filled with “tellers” and very few actual “teachers” any more.

For that reason, serious problem solving and logical thinking skills, are some of the most rare virtues around. Working in nature, where you begin to reap the cause and effects of your own labor, is one of the best habits you will ever develop. Plant a garden, learn how to build things, work with animals, work with your hands and discover for yourself how nature works and the universe operates… but then relate everything to your own life in practical application. It is a good thing to learn from others but learning is not about memorizing, it’s about discovering.

What you want to focus on is discovering principles. Principles are the most precious treasure on earth. they are always hidden beneath and in between what you think you already know. That doesn’t mean that simply working with your hands is the magic. Most people who work with their hands, still haven’t discovered principles.

Only wise and worthy mentors can help to uncover principles for you and then guide you how to discover them through your own practical experience with life. But you must be willing to do the work and discover them for yourself.

Unfortunately, even the vast majority of people who make a living helping to solve problems actually end up creating more problems than they solve because they lack the big-picture of life and reality. That only comes to a small few who have discovered that wisdom is a totally different thing than knowledge. The two are acquired in very different ways. Knowledge is based on information that can be memorized and passed from one person to another. You can stumble upon knowledge through experience but knowledge is all about “answers,” it breeds arrogance and inflated, false pride (most assumed knowledge today is not really knowledge at all but only naïve assumptions, which is really foolishness).

Wisdom on the other hand, is founded on principles. Wisdom is never contented with “answers,” because it knows there is always more…. Wisdom is entirely based on discovering better questions. Answers stop growth, questions demand and perpetuate growth… Since every piece of real truth is totally interdependent on every other truth, there is always more, better, greater improvements to make, regardless of whether you are at the bottom, top or anywhere between-of what you are trying to understand.

The great masters through time, became great masters because they never stopped learning, discovering and evolving. The only way they remain great masters is by never losing track of their leaders, mentors, masters….

Beware, however many, many today believe (and/or try to convince you) that they are wise and flaunt their money, positions, knowledge, influence, etc. Many even believe they have risen above ordinary mortals (talk about ego). But the truly wise and their followers are the ones willing to do what the masses are not willing to do… the hardest work they will ever undertake—their own self evolution. Even though difficult at first, it is only way to live with real fulfillment and genuine happiness that doesn’t fade with the lights and the music….

I have come to call, what everyone wants, but only a few have been willing to discover, the most valuable and precious treasure on earth… “The principles that birth intelligence, lead to wisdom and harness the laws of creation.”

Since you are a creator—that’s what you do, every moment of your life—create your own future reality, You can learn to create something much greater than you have done so far, regardless of how little or far you have come.

Once on that path, you will naturally see what is, over ride your ego that desperately tries to get you to find what will pacify you for the moment, so you don’t have to risk failure, and claim whatever rewards you want most. Intelligently taking those risks is the only path to wisdom and wisdom is the only environment that enables one to solve problems and see the perfect logic in the universe—and align your thoughts and behaviors with it…

There is no way to cut corners to gain wisdom—but it is the great shortcut to super success. Everything else is settle-for. You just must make the decision.

The efforts will pale by comparison to the rewards—IF you recognize and accept that it is all up to you, no one can ever come to your rescue, and then make it a life-style. There is no gimmick or tactic or trick, but once you make those commitments, the right mentors will show up and make all the difference.

Learn to love being uncomfortable, pushing yourself out of your comfort zones IN THE RIGHT DIRECTION and the world will be yours.

Let’s go catch your dreams .

Eldon Grant

How to improve your Logical Reasoning Skills?

Logical Reasoning and thinking is not difficult to develop if you pay attention to certain basic facts such as:

1. Try to differentiate between Observation and Inferences:

To improve your Logical Reasoning skills, it is important to differentiate between observations and inferences. Observation means using your senses such as hearing, seeing, smelling, touching to collect the required data or information. Inference is the conclusion we draw from that observation. Observation is more factual, whereas, inference is one’s opinion based on the observation

How to improve your Logical Reasoning Skills?

Logical Reasoning and thinking is not difficult to develop if you pay attention to certain basic facts such as:

1. Try to differentiate between Observation and Inferences:

To improve your Logical Reasoning skills, it is important to differentiate between observations and inferences. Observation means using your senses such as hearing, seeing, smelling, touching to collect the required data or information. Inference is the conclusion we draw from that observation. Observation is more factual, whereas, inference is one’s opinion based on the observation. Similarly, try to differentiate between established facts and conjectures. Facts are things that are proved or believed to be true based on real occurrences, whereas, a conjecture is a calculated guess which is based on some prior knowledge or incomplete information.

So, once have a clear understanding about facts, observations, inferences, your will be able to derive at good logic's and take better decisions.

2. Types of Statements: Conditional, Converse, Inverse, Contrapositive:

If you wish to enhance your logical reasoning skills, you need to understand the difference between various types of statements such as Conditional, Converse, Inverse or Contrapositive. Conditional statements consists of ‘if then’ analysis, such as If you work hard, then you will get promoted. In a conditional statement, if the premise is true, the conclusion will also be true. The converse statement is when the premise and the conclusion gets reversed such as if you got promoted, then it was because you worked hard. The inverse statement, negates the original premise and the conclusion such as if you do not work hard, you will not get promoted. The contrapositive Statement is either the opposite of the inverse statement or the inverse of the converse statement such as if you didn’t get promoted, it means you didn’t work hard.

3. Understanding the types of conditions:

There are various types of conditions you need to understand to strengthen your Logical Reasoning skills. A Necessary condition is a condition that needs to happen to achieve a certain goal, such as working hard is necessary to get promoted. A sufficient condition is a condition that surely leads to a certain goal such as if you are complacent in your work, you will surely not get promoted. A condition can also be necessary and still not sufficient such as working hard is necessary to get promoted, but there are other factors also to get promoted such as your confidence level, your communication skills, etc. and on the other hand, a condition can also be sufficient but not necessary. Some conditions can also be neither sufficient nor necessary such to get promoted, it is neither sufficient or necessary to work late night everyday.

4. Try to Recognize the Patterns:

Pattern Recognition skills are necessary to improve your logical reasoning skills. This exercise helps you to develop the ability to see a ‘pattern or an order’ in a messy situation. Pattern Recognition strengthens your mental, spatial abilities and your IQ. You must have come across geometrical shapes with some pattern weaving around them or a sequence of numbers, where you need to guess the next number based on a certain pattern or guess which object is odd one out. For taking effective business decisions, recognizing patterns is crucial in various areas such as sales, costs, profits, etc.

5. Create Algorithms and step by step process for solving problems:

You can improve your Logical Thinking by creating algorithms, which is nothing but a step by step process for solving problems. Algorithm gives a clear picture of various conditions and conclusions we derive out of those. This helps us in problem solving process. It defines a sequence of operations and are commonly used in computer programming. One of the most famous algorithms is the Euclid’s algorithm which is used for computing the greatest Common Divisor of two integers (usually positive).

Thanks for the A2A.

They did a study of people once comparing people who studied logic with people who studied chess and found that teaching people chess helped them think logically even more so than teaching them logic.

The reason for that is that our brains are visual, and most of the tenets of logic don't map cleanly into that visual thinking. But chess is both logical and visual.

Ideas such as transposition, overloading of pieces, pawn chain weaknesses and the like play into logic well in ways that mesh with the brains visual processing nature.

So I'd recommend, assuming you want deep skills a

Thanks for the A2A.

They did a study of people once comparing people who studied logic with people who studied chess and found that teaching people chess helped them think logically even more so than teaching them logic.

The reason for that is that our brains are visual, and most of the tenets of logic don't map cleanly into that visual thinking. But chess is both logical and visual.

Ideas such as transposition, overloading of pieces, pawn chain weaknesses and the like play into logic well in ways that mesh with the brains visual processing nature.

So I'd recommend, assuming you want deep skills and are not in a hurry, taking up chess and reading some books on it, then looking at some classic games and playing against people online and against computer opponents and analyzing the games.

You'll find that this increases your ability to start combining logical thoughts.

Then learn things like common fallacies of thinking and other philosophical thoughts.

If you want to go the computer programming route, a good book is this one, Structure and interpretation of computer programs at http://deptinfo.unice.fr/~roy/sicp.pdf which takes things from a logician's perspective.

The most important single questions to start asking yourself are

1. If this is true what else must also be true?

2. If this is true what else must also be false?

3. If this is false what else must also be true?

4. If this is false what else must also be false?

Or, put more succinctly:

"If I know this one (or set of) thing(s), what else can I conclude and also know?"

One other thing I did for a while is played sudoko for fun, and after a couple of weeks started playing without using a pencil (doing the whole thing in my head). That will build up your ability to not only see relationships, but to pile one relationship on top of another.

But it has it's limits (not always easy to transfer the skill to other logic domains) and does get boring after a while, so mix it up.

Not really.

It cannot hurt…but, the logic aspect is a bit different.

With math, you can check to see if the answer is right, and, try something else if it doesn't check, etc. You can do a proof, etc.

With logic, the basic problem is that the brain evolved to take short cuts, as brains are very expensive in calories and nutrients, and, starvation is the most common cause of extinction.

:D

So, we are HARDWIRED to make certain types of mistakes.

Basically, things that “make sense”, and sound “right”, can be wrong, and, wrong in the same way, for the same reasons, because when were were evolving, it did

Not really.

It cannot hurt…but, the logic aspect is a bit different.

With math, you can check to see if the answer is right, and, try something else if it doesn't check, etc. You can do a proof, etc.

With logic, the basic problem is that the brain evolved to take short cuts, as brains are very expensive in calories and nutrients, and, starvation is the most common cause of extinction.

:D

So, we are HARDWIRED to make certain types of mistakes.

Basically, things that “make sense”, and sound “right”, can be wrong, and, wrong in the same way, for the same reasons, because when were were evolving, it didn't matter yet.

This is why optical illusions work at all, for example…we KNOW the types of mistakes the brain makes, and, we can trick it into making them.

So, that’s just a visual example, but, the principle applies to arguments, etc, as well.

So, “learning logic” is less about learning to think, as about learning how NOT TO think… and learning what mistakes our brain WILL make, if we don't reel it in.

Think of it as proactive thinking…LOOKING for the booby traps, by learning what they look and sound like, their properties, etc, so, you can recognize them in any environment.

That means when others present an argument, (Which can be a TV commercial/sale pitch/religious pitch or an editorial or the news, a philosophical argument, etc..)…you are scanning it for booby traps…the things the brain will latch onto and fall for, etc.

It also means scanning what YOU say, for the same thing, to avoid SAYING them too.

:D

Some common examples include confusing causation and correlation, and sunk cost errors, etc.

If you are NOT aware of these sorts of things, they will convince you of things without merit…or, you will say things without merit.

So, a logic class, for example, teaches you the types of errors, or fallacies, and, warns you to be on the lookout.

APPLYING that mental rigor to you life is actually not that easy at first…its easy to let your guard down… but, as it becomes habit, and you drop the human tendency to take the short cuts… you find that many things suddenly become quite clear, and, you can cut through the BS and get to the heart of an issue.

So, math is related to all of this, but, not in the way that you were thinking.

The main way, is that math has its own rules, and, ways of checking your work… but they are not the same rules, or ways, as logic has.

:D

That part about it being your brain and unchangeable is malarky.

I had math phobia for many years, and was convinced that it was one subject I'd never really master. But because so many other subjects came easily to me and it didn't, it was the one that tantalized me and that I had to conquer.

Finally I realized that my problem hadn't been inadequate learning, but inadequate teaching. Never take math from a mathematician unless you too desire to be a mathematician. Take math from an engineer or other tangential practitioner who stresses practical applications.

Math, you see, is only a modeling la

That part about it being your brain and unchangeable is malarky.

I had math phobia for many years, and was convinced that it was one subject I'd never really master. But because so many other subjects came easily to me and it didn't, it was the one that tantalized me and that I had to conquer.

Finally I realized that my problem hadn't been inadequate learning, but inadequate teaching. Never take math from a mathematician unless you too desire to be a mathematician. Take math from an engineer or other tangential practitioner who stresses practical applications.

Math, you see, is only a modeling language. And my introduction to true mathematics came via statistics, which is the ultimate in applied mathematics, because it frankly admits, unlike most of mathematics, that you can know only so much for sure. It joins hands with physics at that point. When I finally realized that all those symbols and equations were just stand-ins for real-world items, math came into focus for me. It became a compact, "lossy" modeling language for the real world. I suddenly had power that most other people declined to seize.

I recommend that you investigate statistics for a starting point. It uses data to tell stories, and considering that you've written that you're a verbal thinker, it may be the most effective path in to the subject of mathematics. In my view, it does the best job of evoking rigorous thinking in non-mathematicians. It has everyday power to predict things, which is why it's widely used in the sciences, economics, and business. You'll quickly run into algebra, of course, which for most of us is the base language and worst learning experience in all of mathematics, but having once tasted the power of statistical thinking, you may be more interested in mastering algebra. A book I often recommend to beginners is The Cartoon Guide to Statistics by Larry Gonick and Wollcott Smith.

Yeah. Contrary to popular opinion intelligence, especially domain specific intelligence, comes via practice and repetition. If you know of a problem and you see a similar problem then you can solve it with ease and given that if you have solved a large number of problems or know the solution to a large number of problems.

I suggest that you keep solving simple puzzles on logical thinking and then your ability to solve problem will increase. However don't get impatient and don't expect results to come fast, this is a main problem in most people. They want to get rich fast, they want to be Bill G

Yeah. Contrary to popular opinion intelligence, especially domain specific intelligence, comes via practice and repetition. If you know of a problem and you see a similar problem then you can solve it with ease and given that if you have solved a large number of problems or know the solution to a large number of problems.

I suggest that you keep solving simple puzzles on logical thinking and then your ability to solve problem will increase. However don't get impatient and don't expect results to come fast, this is a main problem in most people. They want to get rich fast, they want to be Bill Gates without the work which doesn't happen in the real world.

Stick to problems that make you think enough but don't disappoint you. Don't solve a problem for more than a day in the start those are not for you now. Solve the problems that take a day or less and keep solving whenever you can. Do note that you have to only do things that mildly challenge you and if it challenges you too much you might not be interested in doing it anymore.

An analogy I can think of is that the brain is like a muscle and if you exercise it often it gets stronger but if you exercise it too much at a time you get tired and stop being consistent in the exercise. Therefore keep a good healthy pace and take enough breaks.

Apart from this I also suggest getting good sleep and meditation. Both help in increasing you ability to solve problems. Good sleep helps your working memory and so does meditation. Working memory is required to solve problems. Dreams when you sleep also help in consolidating ideas and taking it to long term memory which again helps in problem solving.