Math Textbook Recommendations for a LockSmith Starting College

[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.

 

[Alxb577]

I'd recommend you get on the khan academy and start brushing up on algebra and trig. Try to get through the knowledge map it basically gives you a path on what you need to be proficient in calculus.

 

[SuperDaniel]

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!

Hello Lockie123,

Despite I am not a math specialist, I can suggest you for calculus a classic: Calculus and Analytic Geometry, by George Thomas Jr.

The older edition you can find, the better... I mean, all those editions when the author was still alive... you can find editions from the 50s and 60s, in same cases, cheap on Amazon.

I have a copy from 1953 at home, which was a gift of my uncle, who attended Professor Thomas' classes at the MIT during the early 60s.

As one example of Soviet books you mentioned, I remember Calculus of N. Piskunov, which was suggested by some people here when I attended the university, but, as far as I remember, Thomas' Calculus was much clearer.

I am doing something similar to you, but studying physics: hard job!

Good luck

 

[deluks917]

Do you have any friends who enjoy mathematics. Possibly you could get one of them to teach you. Lots of people love to teach intelligent, motivated students. I for example met approx 4 hours per week with a group of 3 students who wanted to work through Spivak's calculus. As well as answering the occasional skype call to talk something out. We re-served a room in the math department. I did this out of my love for the material and the fact they were good students (one was a friend of mine).

If you cannot find a teacher, the other option is to find another motivated student working on the same material. It is much easier to learn when you have someone to talk to.

 

[megatyler30]

Sorry for the somewhat unrelated post. I'm a high school senior. deluks917, how did you get started teaching those 3 students? I have a similar situation with a professor for statistical mechanics (and hopefully liquid theory before I go off to college) except it's an independent study course although he worked with me over the summer before it started. I already knew the professor before because I had a class with him before. How would I go about finding and asking a professor to do so when I don't know any professors who know the subject (science-based fluid mechanics)? Any input would be very much appreciated.

 

[Lockie123]

Thanks again to everyone for the advice. I'm now making good progress!

 

[neptunemassif]

Congratulations to you on taking a new path! Here are some suggestions for math materials; keep them in your back pocket, hopefully they'll be of use to you.
There's a "Master Math" set of books by Debra Anne Ross (and other authors) that covers basic math all the way to calc. Each book is about $14 and each one covers the subjects fairly well (could use more and better illustrations though). Schaum's outline series was mentioned before; these are extremely useful, but AFTER you take a lesson or are trying to find sample problems as a crutch (around $13 each on Amazon). Might I suggest, once you get to calculus, "The Calculus Lifesaver" by Adrian Banner. Down to Earth language and explains the whats, whys and wherefores, and covers calc1 and 2 as I recall. Another member posted G.B. Thomas - the calc book (13th edition now I think) is a well known and very complete undergrad workhorse text. "The Humongous Book of Calculus Problems" by WM Kelley is also pretty good - side notes and "handwritten" watch-out-for-these kind of remarks.

Aside from texts, consider video-based learning:
As a big proponent of visual learning, especially for foundational, basic math lessons, can't beat a live instructor for tips and tricks. However, next best thing is khanacademy.org - they have an entire k-8 and beyond curriculum, completely free online. They cover everything from arithmetic to multivariable calc (calc 3), and also have lessons in science, physics, economics, and way more - and you can actually follow these all the way through college. The videos go through problems and solutions right in front of you with continuous explanation. On that note, there's also patrickjmt.com (free), and integralcalc on youtube (some free, some pay-to-play).

Some calc websites for good measure:
karlscalculus.org
paul's online math notes, http://tutorial.math.lamar.edu/

As an engineering student, you'll no doubt hit statistics, linear algebra, real analysis, numerical analysis, and of course calc 1/2/3, differential equations, etc. For now don't worry about those, just hit the basics hard. The closer you make the basics second nature to you, the more easy the advanced stuff will come.

Best of luck to you!

 

[saszew]

Congrats on returning to school! I've used this site in my own studies and to help students who I tutored: http://www.purplemath.com. clear, concise explanations. It's a good supplement.
For calculus, I suggest The Humongous Book of Calculus Problems.

 

[davidchandler]

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!

Take a look at the Algebra 1 - Algebra 2 - Precalculus - Calculus sequence by Paul A. Foerster and the text: Geometry: A Guided Inquiry by Chakerian, Crabill, and Stein. I have been recording lessons based on these texts for homeschoolers. They might be suitable for you too. I chose to work with these texts because they have lots of very nice application problems.

 

[Sammbuch]

Have you looked into khanacademy.org ? they have videos on all basic high school math (rules of fractions) up to college math (multivariable calculus and linear algebra). This will fill in many of the gaps or holes in your math education.

 

[Granta1969]

I was in a similar position as you. It had been a while since I had taken math classes. However I am a computer programmer and I know the mathematics involved with what I do, but it was a limited understanding as far as general mathematics was concerned. I wanted to learn more advanced mathematics as I had developed an intersted in programming micro-controllers.

So one day I was in a local donation thrift stores that sells 4 used books for a £1. The selection changes daily and they have all kinds of books and you have to shuffle through piles and piles to find what you want. I had noticed previously that parents often give away their kids textbooks to this charity organization. These books however were something I generally toss to the side and don't pay any attention to.

However, I began to think that I wanted to know what I knew and what I didn't know. I had shuffled through some of these elementary books and realized that I had forgotten some things. I wanted to know, "do I really know as much as say a 13 year old?" I remember when I was in school and at around the age of 13 or 14, I knew a lot about general mathematics. I knew all about Algebra, Geometry (my favorite) and a lot of trig and pre-calculus. But did I still know it? Nope, I sure didn't. Although it was all familiar to me, it had done the old "sand through the hour glass" thing as time had gone by. My ego was in a state of denial for a little while. I felt a little embarrased.

So I'll tell you, don't be too proud to start way down at the bottom. Mathematics is all about "reality." So set your ego to the side and get ready to start from the absolute beginning if necessary. You'll be amazed that some very basic ideas in mathematics have slipped from your memory over the years. It's better that you find out now in the privacy of your home than to realize that you're in way over your head taking an advanced class. Teachers have little tolerance for people who do that because those kinds of students disrupt the flow. Or else you'll just sit there and never ask a question. If you do poorly, it will make all sorts of problems for yourself. Effect your self confidence, etc.

Another thing is that teachers expect you to have a firm understanding of previous material, however, older "adult" learners sometimes are able to by-pass curriculum standards and get themselves into classes of their choice. Sometimes the school will make you take an assesment or an entrance exam.

So do yourself a huge favor and figure out exactly what it is that you know and don't know and start from there. Track down the book shops in town that deal with used books. Those are the best. Check out the thrift stores too because they have discarded used math books that are only generally available to young people in school and are not easily found in retail shops. Use e-bay and gumtree to find math books. I suggest that you work your way up and master at least intermediate algebra and also kow a good deal of geometry before you set foot inside a school.

The books I found most useful were the Official SQA Past Papers with Anwers, type of books. These will let you know in a heart beat if you know as much as a 14 year old, etc. They let you simulate taking an official test. Don't worry if they are a few years old. Also, try to get actual real school textbooks that are aimed at 12 to 16 year olds. If you know what the books are teaching in your community this will give you some confidence. You might be put off a little by how the books communicate and speak on the teen age level with silly pictures. They use analgies that teen agers relate to. "Sally bought herself a new fashion makeup kit containing 8 different coloured lipsticks" Och! Not the kind of analogy that a 40 year old can easily digest. The fact is though, do you know the material?

Also one other little thing: Watch out for any authority figure trying to discourage you. It happens. Age discrimination is real! It's always some mindless pencil pusher in an office that intentionally deprives your of the information you need to be successful.

hope this helps! best of luck!

 

[poor mystic]

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!

Hi :)
I have found that the best teaching resources are at New Zealand/Australian "4th Form" level. Almost any modern book will do.
Usually, the most trouble people have is learning the meaning of division.
Good luck, and feel free to PM me if you have any further questions.
Mark

 

[poor mystic]

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...

I really liked those books too. The "College Algebra, with 1720 solved problems" if I remember correctly, was such a big help.

 

[mathwonk]

I would go to a university science library with a list of topics and books, and browse in the stacks, staying all afternoon or all day reading in them to see which ones are your style. That's what I used to do. It's quiet there too.

In regard to schaum's outline series, in my opinion the older the edition the better (40+ years), so the old ones in a library might be better than what you find for sale at amazon.

 

[clope023]

I would go to a university science library with a list of topics and books, and browse in the stacks, staying all afternoon or all day reading in them to see which ones are your style. That's what I used to do. It's quiet there too.

In regard to schaum's outline series, in my opinion the older the edition the better (40+ years), so the old ones in a library might be better than what you find for sale at amazon.

I agree with this, I have the theoretical mechanics, lagrangian dynamics, and Fourier analysis Schaum's from the 60's and they're probably the best problem books I've worked with. They're occasionally available for slightly steeper prices on amazon.