I want to understand mathematics

[StephanMarcus]

Hello, I'm a 25 year old norwegian male currently studying in my spare time. I have to take a few tests (high school level maths and physics being the most relevant ones) so I can attend university in the near future. My goal is to complete a master's degree in computer science or neuroscience. I haven't really decided which one yet.

So, to my question ...

The subject I'm currently working through is basic algebra and basic geometry. Junior high school level stuff. I am really fascinated by maths, so when I read through these standard books, I ... how do I put this ... I feel uncomfortable because it seems like the authors of the book wants the student to memorize formulas. This makes me *really* uncomfortable because I don't want to simply memorize formulas. I want to understand why they work. I want to understand mathematics. I am sure many of you can relate.

I am wondering if reading through Algebra by Israel M. Gelfand will get me on the right path? Is it a good book? (I will be reading the standard books as well)

Thanks in advance. Sorry if I'm not making any sense. I'm really tired. :)

 

[RaulTheUCSCSlug]

Well reading that book may help, but you have to understand that at the basic level especially junior high level, the math is more like a "given". There is not much to prove, that comes later in math. You could look at a book of proof, but that may be more down the road. For now the important thing would be to solidify your skills in basic math and understand why certain graphs look the way they are, and what you are solving for when you solve systems of equations and what not.

Sorry if that is the answer you are not looking for. There are nice lectures from MIT that might quench your thirst a little more?!

 

[micromass]

YES! Algebra by Gelfand is a great book! If you are interested in math, and especially in why things are true, then read this book. It will definitely set you on the right path. Gelfand really motivates everything carefully, and gives a very deep interpretation of some things which regular high school books take for granted. The only problem with Gelfand is that there are too few problems, but I don't think that should be a reason not to read this book.

 

[MidgetDwarf]

Oakly is also nice. Gelfand is really good.

 

[WWGD]

Oakly is also nice. Gelfand is really good.

So are their books!

 

[StephanMarcus]

Well reading that book may help, but you have to understand that at the basic level especially junior high level, the math is more like a "given". There is not much to prove, that comes later in math. You could look at a book of proof, but that may be more down the road. For now the important thing would be to solidify your skills in basic math and understand why certain graphs look the way they are, and what you are solving for when you solve systems of equations and what not.

Sorry if that is the answer you are not looking for. There are nice lectures from MIT that might quench your thirst a little more?!

I appreciate the answer, though it was not what I wanted to hear. And yes, I have been looking at a few MIT vids, but they expect a certain level, so it's all a bit confusing at the moment. But still good for the occasional breaks from my "real" work. :)

YES! Algebra by Gelfand is a great book! If you are interested in math, and especially in why things are true, then read this book. It will definitely set you on the right path. Gelfand really motivates everything carefully, and gives a very deep interpretation of some things which regular high school books take for granted. The only problem with Gelfand is that there are too few problems, but I don't think that should be a reason not to read this book.

Thanks. I think I'll go with Gelfand's book, then. I have seen a few user reviews in which the person express a dissatisfaction for the lack of answers to the problems in the book. Any idea where I can find a solution set?

Oakly is also nice. Gelfand is really good.

Oakly ... The person who wrote A Mind for Numbers: How to Excel at Math and Science? Is that really a good book? It reminds me of a typical pop science book. Could still be good, I'm just sceptical after being burnt a few times. :)

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What about Mathematics: It's Content, Methods and Meaning. Would that be a better choice? It covers a lot more topics, but I'm thinking about the algebra section.

 

[micromass]

Thanks. I think I'll go with Gelfand's book, then. I have seen a few user reviews in which the person express a dissatisfaction for the lack of answers to the problems in the book. Any idea where I can find a solution set?

Lack of answers is a good thing, because it means you won't be tempted to just read the solution. About half the problems in the book are solved. For the other answers, I would suggest to post your solution here on PF so we can check it or help you if necessary. Having somebody qualified looking over your solution and helping you will help you grow much faster than just looking at the answer. Every criticism will help you grow.

 

[StephanMarcus]

Lack of answers is a good thing, because it means you won't be tempted to just read the solution. About half the problems in the book are solved. For the other answers, I would suggest to post your solution here on PF so we can check it or help you if necessary. Having somebody qualified looking over your solution and helping you will help you grow much faster than just looking at the answer. Every criticism will help you grow.

Yep, I'll certainly keep that that in mind. :) Thanks again.

 

[MidgetDwarf]

I appreciate the answer, though it was not what I wanted to hear. And yes, I have been looking at a few MIT vids, but they expect a certain level, so it's all a bit confusing at the moment. But still good for the occasional breaks from my "real" work. :)
Thanks. I think I'll go with Gelfand's book, then. I have seen a few user reviews in which the person express a dissatisfaction for the lack of answers to the problems in the book. Any idea where I can find a solution set?Oakly ... The person who wrote A Mind for Numbers: How to Excel at Math and Science? Is that really a good book? It reminds me of a typical pop science book. Could still be good, I'm just sceptical after being burnt a few times. :)

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What about Mathematics: It's Content, Methods and Meaning. Would that be a better choice? It covers a lot more topics, but I'm thinking about the algebra section.

https://www.amazon.com/gp/product/B001CD9834/?tag=pfamazon01-20

Find cheaper

 

[StephanMarcus]

https://www.amazon.com/gp/product/B001CD9834/?tag=pfamazon01-20

Find cheaper

Thanks. I've ordered Algebra by Gelfand, so maybe I'll look into it later. :)