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Thread: Math Book Recommendations?

  1. #1

    Math Book Recommendations?

    Can anyone on here recommend their personal favorite math book for beginners? Right now my options seem to be 'Principles Of Mathematics' by Allendoerfer/Oakley and 'Basic Math' by Lang. Any preference between those two and any others that you might recommend? Thank you.

  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by workinprogress View Post
    Can anyone on here recommend their personal favorite math book for beginners? Right now my options seem to be 'Principles Of Mathematics' by Allendoerfer/Oakley and 'Basic Math' by Lang. Any preference between those two and any others that you might recommend? Thank you.
    What level of "math" is to be studied? What level of training does the reader have? What is the reader's age? Why do you feel that the two listed books are your best (or "only"?) options? What is the intended goal of the study?

    Thank you!

  3. #3
    Quote Originally Posted by stapel View Post
    What level of "math" is to be studied? What level of training does the reader have? What is the reader's age? Why do you feel that the two listed books are your best (or "only"?) options? What is the intended goal of the study?

    Thank you!
    Good questions. So: 1) Math from first principles (axioms, sets), beginning with Algebra 1. 2) No formal training other than High School– which he's been out of for years. 3) 25. 4) Those two books have been name-dropped repeatedly by math enthusiasts and math (or math intensive) majors as having the best combination of teaching Math from its roots (i.e., little assumption about previous knowledge) but at the same time doing so in a mature, fairly rigorous fashion (i.e., unlike a 'For Dummies' book). 5) Mastery of concepts that will make him comfortable with equations related to modern physics and thermodynamics.

    Thank you.

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    Whatever book you choose, keep a couple things in mind:

    1) Don't try to go too fast. There are a couple ways to do this organically.
    ----- 1a) Work ALL the problems. I don't necessarily recommend this, but certainly don't just work the ones with the answers in the back.
    ----- 1b) LOOK at ALL the problems. If it looks easy, skip it. (Or maybe do a couple easy ones, just to get a feel for it.) If it looks hard, stop and do that one in detail.

    2) Don't try to go it alone. I often have told home schoolers this one thing, "You can't fake the math. If you can't do the math, get help or don't home school". For you, this translates in to "get local help". Whether it's a paid service, like a Sylvan or a Mathnasium, or it's a competent friend, it may not matter. Just make sure you have someone who can help you through rough spots. We can do a lot, here, but we can't look you in the eye and encourage you in quite the same way as an actual person in person.

    My views. I welcome others'.

    Good luck!!
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  5. #5
    Elite Member stapel's Avatar
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    Quote Originally Posted by workinprogress View Post
    1) Math from first principles (axioms, sets), beginning with Algebra 1...
    Okay, "from first principles" means "graduate-level mathematics, and beyond, being stuff with which the 'great minds' of mathematics have had trouble". "Beginning with Algebra 1" means "middle- or high-school algebra, and onwards" to some point, possible undergraduate college. So these are two very different things.

    If you have no training since high school, so your "foundation" is whatever you can remember from that, then you might want to consider starting with the algebra. Then study trig, maybe some geometry, and then calculus. Throw in some linear algebra, and definitely take a class on "foundations of mathematics" or "proof theory" or some such course. Then you can think about diving into "first principles", such as building the natural numbers from the empty set, the set containing the empty set, the set containing the empty set plus the previous set, etc. (It'll get really weird, really fast.)

    Have fun!

  6. #6
    Quote Originally Posted by stapel View Post
    Okay, "from first principles" means "graduate-level mathematics, and beyond, being stuff with which the 'great minds' of mathematics have had trouble". "Beginning with Algebra 1" means "middle- or high-school algebra, and onwards" to some point, possible undergraduate college. So these are two very different things.

    If you have no training since high school, so your "foundation" is whatever you can remember from that, then you might want to consider starting with the algebra. Then study trig, maybe some geometry, and then calculus. Throw in some linear algebra, and definitely take a class on "foundations of mathematics" or "proof theory" or some such course. Then you can think about diving into "first principles", such as building the natural numbers from the empty set, the set containing the empty set, the set containing the empty set plus the previous set, etc. (It'll get really weird, really fast.)

    Have fun!
    Thanks, man. I appreciate the advice and encouragement. Have you ever read Allendoerfer's 'Principles Of Mathematics'? I really like it.

  7. #7
    Quote Originally Posted by tkhunny View Post
    Whatever book you choose, keep a couple things in mind:

    1) Don't try to go too fast. There are a couple ways to do this organically.
    ----- 1a) Work ALL the problems. I don't necessarily recommend this, but certainly don't just work the ones with the answers in the back.
    ----- 1b) LOOK at ALL the problems. If it looks easy, skip it. (Or maybe do a couple easy ones, just to get a feel for it.) If it looks hard, stop and do that one in detail.

    2) Don't try to go it alone. I often have told home schoolers this one thing, "You can't fake the math. If you can't do the math, get help or don't home school". For you, this translates in to "get local help". Whether it's a paid service, like a Sylvan or a Mathnasium, or it's a competent friend, it may not matter. Just make sure you have someone who can help you through rough spots. We can do a lot, here, but we can't look you in the eye and encourage you in quite the same way as an actual person in person.

    My views. I welcome others'.

    Good luck!!
    Heard on both points. I appreciate the feedback. Working the problems is definitely key. Sometimes I'm going over a worked out problem and I swear I get it, then, two minutes later I'm being asked to do the exact same type of problem on my own and drawing **** near a complete blank. Lol. Thanks again.

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