Math Textbook Recommendations for a LockSmith Starting College

[Lockie123]

After 20 years of being a locksmith, I have decided that I want to get a college degree and I'll be starting next year! As part of my degree, I will be doing two math courses - one in calculus and the other in linear algebra.

However other than addition and subtraction, I don't know much else! I'll need to work my way through K - 12 math textbooks doing topics such as arithmetic, algebra, counting & probability, geometry, number theory, calculus, etc before even touching first year college calculus and linear algebra textbooks!

Could I please get some math textbook recommendations that are clear, proof-based and to the point? I have heard that some Soviet textbooks do what I want but I don't know too much about Soviet textbooks but it does sound interesting!

I do prefer textbooks as I am a bit old fashioned and aren't the best when it comes to using technology! Money also is not a problem so please recommend as many textbooks as needed! If it's better to have a textbook for each field in math then so be it!

 

[moriheru]

Do you have any experience of calculus or advanced algebra, stuff like integrals differential equations and differentiation of functions or limits...? Or basic stuff like inequalitys(ok, probably yes) and so on...?

 

[Lockie123]

Do you have any experience of calculus or advanced algebra, stuff like integrals differential equations and differentiation of functions...?

It has been over 20 years since I've touched a math textbook so I'll need to start from square one! In fact what you just said to me was completely foreign.

 

[moriheru]

I would recommend you read algebra 1 or algebra 2 for dummies (don't laugh), they keep things short but it is a good introduction but, I would not recommend it as a reference. If you have read both or just number 2 you will be (hopefuly) capable of starting with calculus. I would not recommend you read calculus for dummies which is very messie and the examples are very bad, so I would suggest bridging the gap to university mathematics. From then on it's mainly trigonometry and geometry you should cover, but I don't know any book on that...(mocking starts in 3,2,1)

 

[Lockie123]

I would recommend you read algebra 1 or algebra 2 for dummies (don't laugh), they keep things short but it is a good introduction but, I would not recommend it as a reference. If you have read both or just number 2 you will be (hopefuly) capable of starting with calculus. I would not recommend you read calculus for dummies which is very messie and the examples are very bad, so I would suggest bridging the gap to university mathematics. From then on it's mainly trigonometry and geometry you should cover, but I don't know any book on that...(mocking starts in 3,2,1)

Does algebra 1 cover K - 8 arithmetic (decimals, fractions, etc)?

 

[moriheru]

Yes,here is the index:

1.Deciphering signs in Numbers
2.Incorparating Algebraic Properties
3.Making fractions and decimals behave
4.Exploring Exponents
5.Taming rampaging Radicals
6.Simplifying Algebraic Expressions
7.Specializing in Multiplication matters
8.Dividing the long way to simplify algebraic expressions
9.Figuring out factoring
10.Taking the bite out of binomial factoring
11.Factoring trinomials and special polynomials
12.Lining up linear euqations
13.Muscling up to quadratic equations
14.Yielding higher powers
15.Reeling in Radical and Absolute value equations
16.Getting even with inequalitys
...

It goes on until 21 but I would leave them out, those are just some formulas from geometry to calculate areas and so on.

 

[NTW]

I remember fondly the 'Schaum Outline Series' books... I don't know if they are still available. In those books, the theory was clearly explained, in compact paragraphs, there were a few of problems already worked out, and a lot of them to be solved by the reader...

 

[moriheru]

The second book does matrices and arrays, systems of equations, cramers rule. And elaborates on functions, like radical functions and it covers polynomials.

 

[Lockie123]

@NTW I do want the textbooks to be 'to the point' but I don't want a summary. Are those books a summary?

@moriheru I'll have a look into those books. They keep things short, as you said, but is it a summary? I'm trying to find textbooks that are 'clear, proof-based and to the point', I'm not sure if I'm going to find anything!

 

[moriheru]

I don't quite get what you mean, but if you mean covering a large range of basic mathematical topics, yes it does cover most of the basic topics, as you can see by the index. But you shouldn't expect a fully fleshed and detailed book, it's just an introduction, but it introduces you to a large number of topics that you will all need and teaches you the basics, so you can read the details or learn them in university.

 

[moriheru]

Well yes then I would say suggest reading them and they do give you examples but if you want exercises you should by the companion work books(which are cheap). And it has the odd joak. Even thoe now I prefer books dry as dust(Quantum mechanics and kaluza klein theory), I did like the joakes.

 

[Lockie123]

Thank you @moriheru. I welcome any other recommendations!

 

[moriheru]

A ditionary of all formulas is going to come in handy once youve got to calculus. Believe me you will need it! I don't think there are any better and worse dictionary, just more detailed, so I don't have any recommendations.

 

[Feryn]

I would strongly suggest I.M. Gelfand's Algebra and Trigonometry (two separate books). I think these would be exactly what you want: old-school, Soviet, clear rigorous texts. After you're done with those, you would do well to go through Lang's Basic Mathematics.

After that, start calculus. I'd suggest Spivak's Calculus, but you can look around and decide then.

 

[Lockie123]

I would strongly suggest I.M. Gelfand's Algebra and Trigonometry. I think these would be exactly what you want: old-school, Soviet, clear rigorous texts. After you're done with those, you would do well to go through Lang's Basic Mathematics.

After that, start calculus. I'd suggest Spivak's Calculus, but you can look around and decide then.

I just looked up Gelfand's Algebra and Trigonometry - it seems perfect! Would I be able to use them as my main textbooks or are they meant to be supplementary textbooks? Do these textbooks cover all the algebra and trigonometry that is covered in high school?

Could you recommend any books similar to that for arithmetic (K - 8) and the other topics I mentioned? I'll also have a look into the other texts you mentioned.

 

[Feryn]

I just looked up Gelfand's Algebra and Trigonometry - it seems perfect! Would I be able to use them as my main textbooks or are they meant to be supplementary textbooks? Do these textbooks cover all the algebra and trigonometry that is covered in high school?

Could you recommend any books similar to that for arithmetic (K - 8) and the other topics I mentioned? I'll also have a look into the other texts you mentioned.

You can use them as main texts. Serge Lang's Basic Mathematics also covers algebra and trigonometry in somewhat briefer detail. When you're done working with these three, you'll understand these topics better, and in far more detail than they are taught in a regular high school.

These should be sufficient to get you the prerequisites to begin calculus. However, these are more challenging than most books, but I'd advise you to persist and get through- you'll have a richer and deeper grasp of the subject.

EDIT: As for arithmetic, you don't need to get a separate book.

 

[Lockie123]

Thank you @Feryn. I welcome any other suggestions! Like I said, the more, the better!

 

[fourier jr]

After 20 years of being a locksmith, I have decided that I want to get a college degree and I'll be starting next year! As part of my degree, I will be doing two math courses - one in calculus and the other in linear algebra.

However other than addition and subtraction, I don't know much else! I'll need to work my way through K - 12 math textbooks doing topics such as arithmetic, algebra, counting & probability, geometry, number theory, calculus, etc before even touching first year college calculus and linear algebra textbooks!

Could I please get some math textbook recommendations that are clear, proof-based and to the point? I have heard that some Soviet textbooks do what I want but I don't know too much about Soviet textbooks but it does sound interesting!

I do prefer textbooks as I am a bit old fashioned and aren't the best when it comes to using technology! Money also is not a problem so please recommend as many textbooks as needed! If it's better to have a textbook for each field in math then so be it!

In addition to the Gelfand books, Kodaira wrote some high school texts too. I haven't seen more than whatever previews are on Amazon or Google though. Judging by their contents it looks like precalculus & more basic stuff, which seems to be what you're looking for:
http://www.ams.org/cgi-bin/bookstor...=CN&s1=Kodaira_Kunihiko&arg9=Kunihiko_Kodaira

I would also recommend something like Schaum's for mass quantities of problems to solve. There's probably a book with a title like "(so many thousands) of Solved Problems in Precalculus".

 

[Lockie123]

@fourier jr Do you mind telling me what topics are done from K - 12, in order? For example, arithmetic, prealgebra, Algebra I, Geometry I, Algebra II, Geometry II, Proofs & Logic, Discrete Math, Calculus and Geometry III.

Are those all of the topics studied and is that the best order to do it in?

 

[Simon Bridge]

What are the 'best of the best' textbooks to help me learn math from the ground up?

The trouble you will run into is that different people have different learning styles - the best textbooks will be those which best match your learning style. So it is impossible to pick the best of the best for you. What people are doing is trying to suggest textbooks that are the least likely to be rubbish.

Are those all of the topics studied and is that the best order to do it in?

... similar to the above: you should start with something closest to what you already know.
Not all the curriculum subjects get studied by every student - even if they are majoring in mathematics.
Most subjects are taught simultaneously at the same level, and lower levels are taught before higher ones.
The exact details depends on the school (and the country you are in).

However; it is a good idea to find an online course or course summary to guide you.
There are plenty to choose from. You should have a look at several to see what sort of thing fires you up the best.

 

[Lockie123]

@Simon Bridge I haven't found any online course or course summary to guide me. Also, maybe I shouldn't have said 'best of the best' but how about just any recommendations to help me learn math from the ground up using textbooks that are clear, proof-based and to the point?

 

[Feryn]

People have suggested you very good books. Just take whichever you like most, and get started with it. If none takes your fancy, take a look at the textbook listings. Don't be too concerned about the order you're going in, as long as you can follow it.

 

[Lockie123]

@Feryn I already ordered my first book! I cannot wait to start learning again!

 

[Feryn]

@Feryn I already ordered my first book! I cannot wait to start learning again!

Ah, good! Which one?

 

[Lockie123]

@Feryn I decided to go with "Basic Mathematics" by Serge Lang. It looks good! I plan to move on to more complex books afterwards. I just have a quick question though, I am preparing for an engineering degree. When I have the choice between two good textbooks - one skill based, the other theory based, which one should I go for?

 

[Feryn]

@Feryn I decided to go with "Basic Mathematics" by Serge Lang. It looks good! I plan to move on to more complex books afterwards. I just have a quick question though, I am preparing for an engineering degree. When I have the choice between two good textbooks - one skill based, the other theory based, which one should I go for?

If you want to go deep into the subject, take the theory based one. If you just want to know it, so you can apply it: then the skill based one.

 

[Lockie123]

@Feryn Will both textbooks cover the same content though? I assume the skill based one will just be more brief?

 

[fourier jr]

@fourier jr Do you mind telling me what topics are done from K - 12, in order? For example, arithmetic, prealgebra, Algebra I, Geometry I, Algebra II, Geometry II, Proofs & Logic, Discrete Math, Calculus and Geometry III.

Are those all of the topics studied and is that the best order to do it in?

I don't have much experience with math at that level but what youv'e listed so I think other people might have better answers than I can. What you've listed there seems to make sense though fwiw. About those Kodaira books there's the grade 10 one, and then you've got options for the grade 11 ones since that's where they split into theoretical/less-theoretical streams. The descriptions says which is which.

I would also add the Art of Problem Solving series, which I've also been interested in having a closer look at but haven't:
http://www.artofproblemsolving.com/Store/curriculum.php

The title might make it seem like contest-style problem solving but I don't think it is. I think there may be some overlap of the content of some of those books though so make sure you get the right one if you decide to go with any of them.

 

[Dowland]

Gelfand's Algebra book is awesome, I learned tremendous amounts of mathematics doing the problems. However, the problems can be very hard (at least for me) and if you haven't done math for a long time, it's probably going to be a tough start. I would recommend a slightly "softer" book like Harold Jacobs' "Elementary Algebra", it covers everything you need and has been recommended several times on this forum. I haven't read Jacobs' algebra text but I have studied from his geometry text, which I recommend for learning euclidean geometry. If the algebra book is somewhat near as good as his geometry book, then it is worth considering. The two books by Jacobs would probably be very suitable for me to start off with, if I was in a similar position.

BTW, something that I've used a lot for high school mathematics (as a resource on the side) are the video explanations on Khan Academy: https://www.khanacademy.org/math He has videos ranging from the most basic stuff (addition, multiplication) to calculus and linear algebra.

(I'm sorry for any language errors, english is not my native!)

 

[thankz]

you want the saxon books, algebra 1, 2 and advanced math (geometry and trig)
https://www.amazon.com/dp/1600329713/?tag=pfamazon01-20https://www.amazon.com/dp/1600320163/?tag=pfamazon01-20

https://www.amazon.com/dp/160032973X/?tag=pfamazon01-20

I own these so I know their good. I needed to refresh my education and I didn,t know where to start so I bought a book on homeschooling and it led me to these.

 

[thankz]

the order and what you'll need to study is in this post

https://www.physicsforums.com/threads/is-this-a-bs-in-applied-math.764191/#post-4812741

 

[Feryn]

@Feryn Will both textbooks cover the same content though? I assume the skill based one will just be more brief?

That depends on the texts. But, usually, yes. There will be a lot more handwaving in the skills text, so yes, "briefer" in that manner. But some skills texts explain more about applications than do theory ones. Don't worry too much about these, you'll pick it up as go along- and see which suits your learning style best.

 

[Simon Bridge]

@Simon Bridge I haven't found any online course or course summary to guide me. Also, maybe I shouldn't have said 'best of the best' but how about just any recommendations to help me learn math from the ground up using textbooks that are clear, proof-based and to the point?

You are already getting that ;) - everyone has their favorites. What 'm showing you is in parallel with what they are doing.
For curriculum guidelines - you can usually just google for the secondary curriculum for your jurisdiction - I'm guessing: USA?
http://en.wikipedia.org/wiki/Mathematics_education_in_the_United_States#Curricular_content
... that gives an overview and a starting point. You may prefer a more integrated approach - so have a look at what other countries do.

You can also look on many High School websites and they tend show you what they cover and roughly what order ... how long the typical courses take and things like that.

 

[Lockie123]

Thanks for the help so far! @Feryn In regards to the theory based textbooks, does that mean some theory based textbooks don't show you or get you to work out how to apply the knowledge to questions? Often are the questions much more difficult in skill based or theory based textbooks? Lastly, will the skill based or theory based textbook help me more with an engineering degree? The professors emphasised to me that I really need to know my stuff and know why things are the way they are as there will be proofs in first year college math.

 

[Feryn]

Thanks for the help so far! @Feryn In regards to the theory based textbooks, does that mean some theory based textbooks don't show you or get you to work out how to apply the knowledge to questions? Often are the questions much more difficult in skill based or theory based textbooks? Lastly, will the skill based or theory based textbook help me more with an engineering degree? The professors emphasised to me that I really need to know my stuff and know why things are the way they are as there will be proofs in first year college math.

It varies from text to text. Typically, as I said skill books will focus more on applications, and be more computational than those which emphasize theory. Most textbooks will not be entirely theoretical, or application-based - falling somewhere in between, with emphasis on one.

As to difficulty, I'd say skill based would be more memorization and following the required steps, while theory would be more proof and understanding based. As an engineering student, for advanced mathematics, you'll be using a applications or skill based text, rather than a theoretical one, because there's too much. If you're interested in the underlying theory, you can always look it up yourself.

Ideally, you'd prefer to know the theory behind all math - but it simply isn't practical, from what I've heard. So, get your theory well-grounded till calculus, and from further on- you can rely on application based stuff, and look up the theory if you want to. You aren't restricted to only one text.

It all depends on what you want to do.