I want to start studying math to train myself to think more logically. Can anyone recommend good books?

Though math is a perfectly logical format, it doesn’t necessarily apply to real life.

I’d recommend “Paradigms Lost” which delves into Popper’s expositions on the scientific method. Learning how to subtract assumptions from critical models is the real key to purely logical thinking.

I haven’t really got an up-to-date answer, but there are a couple of things to say.

It’s not clear what you mean by zero level. Apparently you can count, and are familiar the concept of zero. It took mankind a long time to invent a symbol for zero. So perhaps basic arithmetic is your zero level. You need to somehow make a map of your task, and the first thing is to establish what you know and don’t know. An old book, Prelude to Mathematics by WW Sawyer is quite a good place to start to get an idea of where you are, the direction you are going, and the kinds of thought processes involved. Concre

I haven’t really got an up-to-date answer, but there are a couple of things to say.

It’s not clear what you mean by zero level. Apparently you can count, and are familiar the concept of zero. It took mankind a long time to invent a symbol for zero. So perhaps basic arithmetic is your zero level. You need to somehow make a map of your task, and the first thing is to establish what you know and don’t know. An old book, Prelude to Mathematics by WW Sawyer is quite a good place to start to get an idea of where you are, the direction you are going, and the kinds of thought processes involved. Concrete Mathematics by Knuth et al, is also a popular foundation.

The only way to know what is involved to reach graduate level is to look at degree courses, at the lecture courses that comprise the degree, and at the reading list for the lecture course. But textbooks cover far more material than a course would teach. The teacher would normally direct you to the parts you need to master. The rest is there to give teachers flexibility, and students reference material that will be accessible as needed after the course is done.

So I’d recommend using online courses to guide your study. You need a framework to hang the individual bits of maths on to, and you need to know what you can skip first time round in the textbooks. Us the lecture, and dip in to the books as appropriate. Of course if you’re a genius, you can read the textbooks like a novel, but chances are you’ll want to focus.

If you are trying to do it without a tutor, you should find textbooks with problems and worked solutions to compare with your own. When you’re really stuck, you can ask Quora.

You can probably do the whole thing with twenty textbooks altogether, using maybe three at any one time.

To develop logical skill you have to practice as many as you can. Find a programming problem (e.g. Programming Competition,Programming Contest,Online Computer Programming) , try to write down the algorithm, then write it in any programming language which you understand. After that, compare your solution with others solution. Looking at the other people solution will make you looking to the problem from different angle, and can be useful to measure at which level of your current skill are.

How do I improve logic building skills in a Programming language?

Everyth

To develop logical skill you have to practice as many as you can. Find a programming problem (e.g. Programming Competition,Programming Contest,Online Computer Programming) , try to write down the algorithm, then write it in any programming language which you understand. After that, compare your solution with others solution. Looking at the other people solution will make you looking to the problem from different angle, and can be useful to measure at which level of your current skill are.

How do I improve logic building skills in a Programming language?

Everything can be learned, as long as you're willing to apply yourself and commit to it.
Those are two very different skillsets though (logic and creativity, from your original question's title). You could be a very logical yet totally non-creative person.
Improve your Creativity

The best way to work on your creativity is to try new things, and to get out of your confort zone.
As an aside: creativity is a way more complex concept than one may think, and attempts at measuring it and developing it havebeen around for quite some time.
Improve your Logic Skills

Take Courses in Formal Logic Theory
I was already a pretty decent programmer when I was invited to follow another master's coursework which included a course on formal logic. Being not really a "formal CS theory guy", that made me discover and completely new side of the field.
What about following the next sessions of these online courses? (amongst many, many others, some taught by famed professors... or their TAs)

Books, TextBooks and Research

  • Introduction to Formal Logic - Peter Smith
  • Agorithms - Robert Sedgewick

Programming Exercises and Code Katas

Coding Challenges

Practice, Practice, Practice

"Good judgment comes from experience, and a lot of that comes from bad judgment."

Much of philosophy won’t make much sense without reading it in the order developed, so if you have time get any general introduction (wikipedia is good, too) and start with Plato and Socrates. Read entries on metaphysics, ontology, ethics, political philosophy, epistemology, rationalism, idealism, monism, dualism, empiricism. Given your interests you could jump straight to a “Philosophy of Mathematics” book (I haven’t read enough to tell you the best). Russell and Witgenstein worked on the issues of deriving general philosophical statements from math or math-like axioms. Read about Godel’s pro

Much of philosophy won’t make much sense without reading it in the order developed, so if you have time get any general introduction (wikipedia is good, too) and start with Plato and Socrates. Read entries on metaphysics, ontology, ethics, political philosophy, epistemology, rationalism, idealism, monism, dualism, empiricism. Given your interests you could jump straight to a “Philosophy of Mathematics” book (I haven’t read enough to tell you the best). Russell and Witgenstein worked on the issues of deriving general philosophical statements from math or math-like axioms. Read about Godel’s proof. Add a bit on chaos theory, the nature of causation, the indeterminate nature of reality at the quantum level, debates about the Copenhagen interpretation, arguments about whether the universe is based on information at its base (including space-time), information theory (“The Information” is good), read some of the articles at Edge.org, check out Max Tegmark’ “Our Mathematical Universe”.

You can visit my page to find the book you are looking for and download it for free. Click this link

The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

This is, quite simply, the best and most popular puzzle book ever published in the Soviet Union. Since its first appearance in 1956 there have been eight editions as well as translations from the original Russian into Ukrainian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold.
Part of the reason for the book's success is its marvelously varied assortment of brainteaser

You can visit my page to find the book you are looking for and download it for free. Click this link

The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

This is, quite simply, the best and most popular puzzle book ever published in the Soviet Union. Since its first appearance in 1956 there have been eight editions as well as translations from the original Russian into Ukrainian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold.
Part of the reason for the book's success is its marvelously varied assortment of brainteasers ranging from simple "catch" riddles to difficult problems (none, however, requiring advanced mathematics). Many of the puzzles will be new to Western readers, while some familiar problems have been clothed in new forms. Often the puzzles are presented in the form of charming stories that provide non-Russian readers with valuable insights into contemporary Russian life and customs. In addition, Martin Gardner, former editor of the Mathematical Games Department,
Scientific American, has clarified and simplified the book to make it as easy as possible for an English-reading public to understand and enjoy. He has been careful, moreover, to retain nearly all the freshness, warmth, and humor of the original.
Lavishly illustrated with over 400 clear diagrams and amusing sketches, this inexpensive edition of the first English translation will offer weeks or even months of stimulating entertainment. It belongs in the library of every puzzlist or lover of recreational mathematics.

First of all a big thumbs up for atleast admitting that you need to improve your maths. Trust me it takes tons of courage to openly admit such things. So….definitely you can improve because you don’t lack courage.

Well, i feel you should contemplate and figure out that from exactly which class you lost it in maths. Still, i personally suggest you to pick up NCERTs from 6th standard onwards. The key should not be on finishing everything rather focus on building concepts. NCERTs are written in a very lucid launguage and understanding will never be a problem.

Set a realistic goal for yourself…and j

First of all a big thumbs up for atleast admitting that you need to improve your maths. Trust me it takes tons of courage to openly admit such things. So….definitely you can improve because you don’t lack courage.

Well, i feel you should contemplate and figure out that from exactly which class you lost it in maths. Still, i personally suggest you to pick up NCERTs from 6th standard onwards. The key should not be on finishing everything rather focus on building concepts. NCERTs are written in a very lucid launguage and understanding will never be a problem.

Set a realistic goal for yourself…and just never give up. You have this courage of openly admitting your weaknes, so you definitely have that element in you which will provide you with the required fillip to overcome this weakness. Its all within you…Just explore the ocean of courage you have within you.

All the best.

It is not in the books. It is in you. The power of your concentration and observing every little thing that you see! With days of such a habit, you feel it easier to do the regular works in the simplest of the ways by itself in order to save your time.

Besides this, logical thinking improves with the practice of imagining and visualizing things in different ways possible by the mankind.

Coming to the point of math, it is more based on application of concepts in real life that you need to focus on rather than just learning bookish formulas. The more speed you are, the big expert you become.

In cas

It is not in the books. It is in you. The power of your concentration and observing every little thing that you see! With days of such a habit, you feel it easier to do the regular works in the simplest of the ways by itself in order to save your time.

Besides this, logical thinking improves with the practice of imagining and visualizing things in different ways possible by the mankind.

Coming to the point of math, it is more based on application of concepts in real life that you need to focus on rather than just learning bookish formulas. The more speed you are, the big expert you become.

In case, you are searching for books, R.S. Aggarwal’s or Arun Sharma’s Editions in Logical thinking and Reasoning books can help you increase your problem solving skills in the least time with good explanation methods.

Happy learning!

One of the standard Calculus and Analytic Geometry intro texts in college or advanced placement is the G.B. Thomas Calculus. I grew up on the 3rd and 4th edition - I think they're up to the 13th edition. You can actually get a text "based on the Thomas Calculus" here:Thomas Calculus 12th Edition PDF | Free Download (it's not actually the Thomas text by Thomas).

This is also a pretty interesting pdf to prepare you: https://www.math.wisc.edu/~jeanluc/lecturing/lecs-221_robbin.pdf

And this site has some great links to all kinds of math books: Mathematical Ideas That Shaped The World

I think first you should decide what kinds of topics you are interested in and where you want to take your mathematics. Whether this is geometry, calculus or algebra, it is up to you to decide.

If you have almost no knowledge in maths, I would recommend you start with familiarising yourself with the order of operations (BIDMAS). Then afterwards probably basic geometry (area, perimeter, shapes etc.)

Remember this choice is ultimately up to you.

Then I recommend you go onto Khan Academy.

Khan Academy is an online learning platform which gives practice questions, video tutorials and worked examples.

I think first you should decide what kinds of topics you are interested in and where you want to take your mathematics. Whether this is geometry, calculus or algebra, it is up to you to decide.

If you have almost no knowledge in maths, I would recommend you start with familiarising yourself with the order of operations (BIDMAS). Then afterwards probably basic geometry (area, perimeter, shapes etc.)

Remember this choice is ultimately up to you.

Then I recommend you go onto Khan Academy.

Khan Academy is an online learning platform which gives practice questions, video tutorials and worked examples. The video tutorials goes in depth to ensure you really understand the material and how the whole operation works.

It will also provide you with questions and topics which are suitable for your level to ensure you don't get lost.

Consider getting the book: Mathematics: the Science of Patterns, by Dr. Keith Devlin (1997, Scientific American Publications). It shows the order and beauty of mathematics in several broad areas.

You can start with:

  1. Alice in Wonderland
  2. Aristotle
  3. Heuristics overview
  4. Infinity
  5. Martin Gardner books
  6. Alan Sokal's writings on science, philosophy and culture
  7. Even physics