Reddit mentions of Basic Mathematics

Serge Lang's Basic Mathematics. It covers all of mathematics in a comprehensive manner until calculus.

https://www.amazon.ca/Basic-Mathematics-Serge-Lang/dp/0387967877

I had to deal with the no internet thing for some time.
Find some place with free wi-fi(you are using phone?).
Download ebook/pdf reader, FBreader + PDF plugin is good (Assuming that you are using Android phone).
Install Firefox and this add-on Save Page WE, it also work for phones (tested with Android).

Then you can save pages from some of these web sites or Wikipedia:

• mathsisfun
  
  
• purplemath
  
  
• sosmath
  
  
• tutorial.math.lamar
  
  
• themathpage
  
  
  
  
  
  Poor man's library:
  
  http://gen.lib.rus.ec/
  http://b-ok.org/
  https://archive.org/
  
  Some books:
  
  [Harold Jacobs - Elementary Algebra] (https://www.amazon.com/Elementary-Algebra-Harold-R-Jacobs/dp/0716710471) (that's the most friendly and still not bullshit introduction I was able to find)
  
  [Basic Mathematics by Serge Lang] (https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877) - Make sure that you understand the first 100-150 pages from the first book if you want to start this one.
  
  Precalculus by David Cohen - Lang's Basic Mathematics is harder (and much more interesting) than this...
  
  Use the three web sites written above to download them. PDF for better performance (and some times quality) on cheap phone, epub/djvu for the smaller size.
  
  I think that free wi-fi will be easy to find. Reading books wouldn't be like watching videos but you will actually learn more. Compass, straightedge and protractor would be really useful.
  

For the very basics (and more), I can highly recommend you Professor Leonard on YouTube.

>What books would you recommend?

How about doing your own research?

Google.com -> book site:reddit.com/r/learnmath



Anyways, take a look at Basic Mathematics by Serge Lang. This is what I'm learning with right now, it's really great.

Mathematics, a learning map

Edit:

Ehm, or take a look at your own thread from a year ago.

https://www.reddit.com/r/learnmath/comments/46xdpp/learning_math_from_scratch_all_by_myself/

Hi. The book Basic Mathematics by Serge Lang covers high school math in a way that is similar to most texts on higher mathematics, with theorems and proofs. As such, I think it would make a great stepping stone to higher maths, and some reviewers on Amazon agree. It gives you a solid foundation, and a little bit of an idea what's in store for you if you choose to pursue math. I think it would be a great place to start.

Send me a PM if you need help obtaining (a digital version of) the book.

Indeed; you may feel that you are at a disadvantage compared to your peers, and that the amount of work you need to pull off is insurmountable.

However, you have an edge. You realize you need help, and you want to catch up. Motivation and incentive is a powerful thing.

Indeed, being passionate about something makes you much more likely to remember it. Interestingly, the passion does not need to be a loving one.

A common pitfall when learning math is thinking it is like learning history, philosophy, or languages, where it doesn't matter if you miss out a bit; you will still understand everything later, and the missing bits will fall into place eventually. Math is nothing like that. Math is like building a house. A first step for you should therefore be to identify how much of the foundation of math you have, to know where to start from.

Khan Academy is a good resource for this, as it has a good overview of math, and how the different topics in math relate (what requires understanding of what). Khan Academy also has good exercises to solve, and ways to get help. There are also many great books on mathematics, and going through a book cover-to-cover is a satisfying experience. I have heard people speak highly of Serge Lang's "Basic Mathematics".

Finding sparetime activities to train your analytic and critical thinking skills will also help you immeasurably. Here I recommend puzzle books, puzzle games (I recommend Portal, Lolo, Lemmings, and The Incredible Machine), board/card games (try Eclipse, MtG, and Go), and programming (Scheme or Haskell).

It takes effort. But I think you will find your journey through maths to be a truly rewarding experience.

Do not enroll in a precalculus class until you have a solid grasp on the foundations of precalculus. Precalculus is generally considered to be the fundamentals required for calculus and beyond (obviously), and a strong understanding of precalculus will serve you well, but in order to do well in precalculus you still need a solid understanding of what comes before, and there is quite a bit.

I do not mean to sound discouraging, but I was tutoring a guy in an adult learning program from about December 2017-July 2018...I helped him with his homework and answered any questions that he had, but when he asked me to really get into the meat of algebra (he needed it for chemistry to become a nurse) I found a precalculus book at the library and asked him to go over the prerequisite chapter and it went completely over his head. Perhaps this is my fault as a tutor, but I do not believe so.

What I am saying is that you need a good foundation in the absolute basics before doing precalculus and I do not believe that you should enroll in a precalculus course ASAP because you may end up being let down and then give up completely. I would recommend pairing Basic Mathematics by Serge Lang with The Humongous Book of Algebra Problems (though any book with emphasis on practice will suffice) and using websites like khanacademy for additional practice problems and instructions. Once you have a good handle on this, start looking at what math courses are offered at your nearest CC and then use your best judgment to decide which course(s) to take.

I do not know how old you are, but if you are anything like me, you probably feel like you are running out of time and need to rush. Take your time and practice as much as possible. Do practice problems until it hurts to hold the pencil.

Basic Mathematics by Serge Lang.

https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877

If you’d like a physical textbook, I’d recommend Basic Mathematics by Serge Lang, a celebrated mathematician and teacher. It’s an oldie but a goodie. https://www.amazon.com/dp/0387967877/

If you progress past that and want to refresh your calculus, it’s hard to go wrong with James Stewart’s Calculus. https://www.amazon.com/dp/B00YHKU50E/

The Art of Problem Solving has algebra books that focus a bit more on learning through problem solving than your average textbook. Also, Serge Lang's Basic Mathematics is a book about high school math written at a fairly high level.

I agree that there's an unfortunate tendency toward "cookbook mathematics" out there. On the topic you brought up, note that there isn't a general method of factoring polynomials by hand, so there isn't necessarily anything they could teach you that would subsume all other knowledge. However, I'd say learning by solving problems rather than memorizing unmotivated algorithms is better when possible.

Lang's Basic mathematics might cover what you need.

https://www.amazon.fr/gp/product/0387967877/ref=ppx_yo_dt_b_asin_title_o09_s03?ie=UTF8&psc=1

Il part vraiment de 0 et présente la construction des mathématiques à partir d'éléments très simples. Il faut comprendre l'anglais par contre, il y a peut-être des traductions.

I've read some good reviews of Basic Mathematics by Serge Lang. It should prepare the reader for calculus.

Otherwise, many online and free books are already available. Here you find a list of free books approved by the American Institute of Mathematics.

If you want to understand the WHY, then you need to read proofs and at least be familiar with basic concepts of logic. I've found this site really helpful. It's a source for definitions and proofs.

What class were you previously in? What class are you going to now? Honestly, if you just practice an hour a day going through a textbook like Lang's Basic Mathematics, then you'll be fine. The summer is a great time to not only review but to get ahead. Bored of your previous material? Go learn something new!

I think Basic Mathematics is basically a precalculus text. I can't stand normal textbooks, everything is disconnected and done for you. This is written by one of the best mathematicians and will provoke thought and understanding. He knows his audience too, he's good with kids, check out his book Math! Encounters with High School Students. He's also written a 2-volume calculus text that I know has been used well in high school settings.

There are some really good books that you can use to give yourself a solid foundation for further self-study in mathematics. I've used them myself. The great thing about this type of book is that you can just do the exercises from one side of the book to the other and then be confident in the knowledge that you understand the material. It's nice! Here are my recommendations:

First off, three books on the basics of algebra, trigonometry, and functions and graphs. They're all by a guy called Israel Gelfand, and they're good: Algebra, Trigonometry, and Functions and Graphs.

Next, one of two books (they occupy the same niche, material-wise) on general proof and problem-solving methods. These get you in the headspace of constructing proofs, which is really good. As someone with a bachelors in math, it's disheartening to see that proofs are misunderstood and often disliked by students. The whole point of learning and understanding proofs (and reproducing them yourself) is so that you gain an understanding of the why of the problem under consideration, not just the how... Anyways, I'm rambling! Here they are: How To Prove It: A Structured Approach and How To Solve It.

And finally a book which is a little bit more terse than the others, but which serves to reinforce the key concepts: Basic Mathematics.

After that you have the basics needed to take on any math textbook you like really - beginning from the foundational subjects and working your way upwards, of course. For example, if you wanted to improve your linear algebra skills (e.g. suppose you wanted to learn a bit of machine learning) you could just study a textbook like Linear Algebra Done Right.

The hard part about this method is that it takes a lot of practice to get used to learning from a book. But that's also the upside of it because whenever you're studying it, you're really studying it. It's a pretty straightforward process (bar the moments of frustration, of course).

If you have any other questions about learning math, shoot me a PM. :)

Serge Lang's Basic Mathematics is probably what you're looking for.

The Art of Problem Solving contest prep books might also be useful.

If you're just struggling with proofs, Velleman's How to Prove It is the book to get.

Since you hope to study mathematics more seriously, I would look into this book link.

It's an excellent book that treats high school/basic college mathematics in an "adult" way. By adult I mean in the way that mathematicians think about it.
(The fun thing about Lang is that you can read only his books and get pretty much a high school through advanced graduate education).

If you feel confident in your basic addition, subtraction, multiplication and division skills, I would start with an in-depth study of algebra using a rigorous book like Gelfand and Shen's Algebra or Lang's Basic Mathematics. The reason why I'd pick a book like this over an SAT prep book is because the SAT book will be concerned whether you can get the right answer to a problem, while the books I suggested focus on teaching you why the things you're learning are true.

hey i found something you need

I like to reccommend Basic Mathematics by Serge Lang. It will take you exactly from addition and subtraction to a prepared state for calculus and beyond. Don't let the name fool you though, it is a rigorous study, but with an honest effort you will do well.

Basic Mathematics by Serge Lang is one. Not free, though.

Serge Lang's Basic Mathematics is probably the place to start if its been 8 years.

I've heard good things about Serge Lang's Basic Mathematics. It's pre-calculus geometry and algebra mainly I think, but it treats you like a grown-up.

The two books already mentioned sound awesome, but if you ever wanted a textbook with a formal approach to mathematics (written by a well-known and respected mathematician), check out Basic Mathematics by Serge Lang.

This is more for anyone reading who would like to continue on to a math or perhaps a physics major. The book takes you from elementary algebra and geometry all through pre-calculus; basically the only book you should need to prepare you for calculus and elementary linear algebra.

You might find this book to be a good place to start: Algebra, by Gelfand and Shen.

Another book in a similar vein might be Basic Mathematics by Serge Lang.

I haven't used either of these books myself, but I came across them recently, and it looks like they might be among the few titles that cover high-school math in the way that you describe (they were written by prominent research mathematicians).

You might consider using the materials on Khan Academy (articles, videos, and exercises) to structure your studies, since these may be more closely aligned with current standards in the U.S. Then, as you go along, you can use these books as supplements (e.g. if you feel that a different perspective on a particular topic might be helpful).

My two cents

1. Maths is difficult. There isn't one of us who at some point has not struggled with it
   
2. Maths should be difficult. The moment you find it easy you are not pushing yourself!
   
   If you want to improve your skills you can do two things in the short term -- read and practice.
   
   I would recommend Basic Mathematics by Lang (it gets mentioned a lot around here). Or if you are interested in higher math look at How to Prove It by Velleman
   
   The great thing is that both include exercises.

http://www.amazon.ca/Basic-Mathematics-Serge-Lang/dp/0387967877

First, please make sure everyone understands they are capable of teaching the entire subject without a textbook. "What am I to teach?" is answered by the Common Core standards. I think it's best to free teachers from the tyranny of textbooks and the entire educational system from the tyranny of textbook publishers. If teachers never address this, it'll likely never change.

Here are a few I think are capable to being used but are not part of a larger series to adopt beyond one course:
Most any book by Serge Lang, books written by mathematicians and without a host of co-writers and editors are more interesting, cover the same topics, more in depth, less bells, whistles, fluff, and unneeded pictures and other distracting things, and most of all, tell a coherent story and argument:

Geometry and solutions

Basic Mathematics is a precalculus book, but might work with some supplementary work for other classes.

A First Course in Calculus

For advanced students, and possibly just a good teacher with all students, the Art of Problem Solving series are very good books:
Middle & high school:
and elementary linked from their main page. I have seen the latter myself.

Some more very good books that should be used more, by Gelfand:

The Method of Coordinates

Functions and Graphs

Algebra

Trigonometry

Lines and Curves: A Practical Geometry Handbook

Okay. So..


You speak of this book I assume. Which is intended to be used by students in H.S. Yet you are familiar with abstract algebra? I understand abstract algebra has many levels to it. But how far did you go? Was it so close that you were touching on topographies or statements?

I'm very confused here. You're concerned about your math. But yet you're reading a calculus prep book?

What is an IT college exactly? Are you a freshman or sophomore at a Uni? And it happens that you are referring to your department? Or are you referring to a technical college / school?

These questions are to satisfy my assumptions. Optional at best.



As a math major with a CS minor in my uni, which is something I'm in the process of. I am required pre-algebra, algebra, pre-calc, calc, calc 1, calc 2, calc 3, abstract algebra, linear algebra, discreet math, some general programming classes involving these prerequisite math courses, and some other math classes I cannot remember.

Abstract algebra, in my opinion is something of a higher level language. So this should explain my confusion here.

The Serge Lang book looks to be pretty expensive on Amazon, is it worth it?

Thank you for the recommendations, the Gelfand books look like they're worth checking in to!

Here is a good book on trigonometry.

Here is one for algebra.

Here's another

I've heard people recommend Kiselev's Geometry, on a physics forum. Warning, though; Kiselev's Geometry series(in English) is translated from Russian.

Here's the link to where I got all these resources(I also copy-pasted what's in the link down below; although, I did omit a few entries, as it would be too long for this reddit comment; click the link to see more resources):

https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/

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Note: Alternatively, you can order Kiselev's geometry series from http://www.sumizdat.org/

Geometry I and II by Kiselev

http://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202

http://www.amazon.com/Kiselevs-Geometry-Book-II-Stereometry/dp/0977985210

> If you do not remember much of your geometry classes (or never had such class), then you can hardly do better than Kiselev’s geometry books. This two-volume work covers a lot of synthetic (= little algebra is used) geometry. The first volume is all about plane geometry, the second volume is all about spatial geometry. The book even has a brief introduction to vectors and non-Euclidean geometry.

The first book covers:

• Straight lines
  
  
• Circles
  
  
• Similarity
  
  
• Regular polygons and circumference
  
  
• Areas
  
  The second book covers:
  
  
• Lines and Planes
  
• Polyhedra
  
• Round Solids
  
• Vectors and Foundations
  
  > This book should be good for people who have never had a geometry class, or people who wish to revisit it. This book does not cover analytic geometry (such as equations of lines and circles).
  
  ____
  
  

  Geometry by Lang, Murrow
  

  
  http://www.amazon.com/Geometry-School-Course-Serge-Lang/dp/0387966544
  
  > Lang is another very famous mathematician, and this shows in his book. The book covers a lot of what Kiselev covers, but with another point of view: namely the point of view of coordinates and algebra. While you can read this book when you’re new to geometry, I do not recommend it. If you’re already familiar with some Euclidean geometry (and algebra and trigonometry), then this book should be very nice.
  
  The book covers:
  
  

• Distance and angles
  
  
• Coordinates
  
  
• Area and the Pythagoras Theorem
  
  
• The distance formula
  
  
• Polygons
  
  
• Congruent triangles
  
  
• Dilations and similarities
  
  
• Volumes
  
  
• Vectors and dot product
  
  
• Transformations
  
  
• Isometries
  
  > This book should be good for people new to analytic geometry or those who need a refresher.
  
  > Finally, there are some topics that were not covered in this book but which are worth knowing nevertheless. Additionally, you might want to cover the topics again but this time somewhat more structured.
  
  > For this reason, I end this list of books by the following excellent book:
  
  

  Basic Mathematics by Lang
  

  
  http://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877
  
  > This book covers everything that you need to know of high school mathematics. As such, I highly advise people to read this book before starting on their journey to more advanced mathematics such as calculus. I do not however recommend it as a first exposure to algebra, geometry or trigonometry. But if you already know the basics, then this book should be ideal.
  
  

• The book covers:
  
  
• Integers, rational numbers, real numbers, complex numbers
  
  
• Linear equations
  
  
• Logic and mathematical expressions
  
  
• Distance and angles
  
  
• Isometries
  
  
• Areas
  
  
• Coordinates and geometry
  
  
• Operations on points
  
  
• Segments, rays and lines
  
  
• Trigonometry
  
  
• Analytic geometry
  
  
• Functions and mappings
  
  
• Induction and summations
  
  
• Determinants
  
  > I recommend this book to everybody who wants to solidify their basic knowledge, or who remembers relatively much of their high school education but wants to revisit the details nevertheless.
  
  _____
  
  More links:
  
  https://math.stackexchange.com/questions/34442/book-recommendation-on-plane-euclidean-geometry
  
  Note: oftentimes, you can find geometry book recommendations( as well as other math book recommendations) in stackexchange; just use the search bar.
  
  __
  
  https://www.physicsforums.com/threads/geometry-book.727765/
  
  https://www.physicsforums.com/threads/decent-books-for-high-school-algebra-and-geometry.701905/
  
  https://www.physicsforums.com/threads/micromass-insights-on-how-to-self-study-mathematics.868968/