"100% Mathematical Proof" vs Vellmen's "How to Prove it"
Hello, I'm looking for books that teach proof methods and techniques. I know Vellemen's book is a popular choice but a few dissenting reviews among unanimous praise, on its amazon page, caught my attention. Like this one:
And here are...
I think the most fun and best way to learn math and physics is by doing challenging problems that require ingenuity and resourcefulness. Those problems should also illuminate the most important topics as well. A book that does that very well is Putnam and Beyond and a few other math Olympiad...
Oh I definitely agree that "The Elements of Style" offers good advice. I like how concise the book is and how lean Strunk's writing is. I think that's why the book appeals to so many people in the first place. There is a certain grace to its brevity. But its brevity is ultimately its undoing. He...
I'd stay away from books such as "Elements of Style." My writing is terrible and that book or similar books like "On Writing Well" did not help improve it one iota. The advice was too vague for me to put into practical use. Clear thinking and clear writing go hand in hand so I think it's best to...
Personally I admire mathboy's ability to study 12+hours a day, especially since he does it out of pure enjoyment. The only time I devoted that much time a day to something was when I was really into MMORPGS as a teenager. I hope I can find that sort of dedication and passion as well.
That...
There's one book that I know of that's laid out exactly how you have said in your OP. I'm sure you know about it. "The Principles of Mathematics by Allendoerfer and Oakley. At the beginning it definitely starts out conversational as it introduces basic mathematical logic and set theory but gets...
Whoops... I need to read more carefully. I didn't realize that that was the distributive law because I always write it down with the multiplication signs in between a and b. But actually... That makes things a TON clearer. That and particularly number 1 makes it clear.
I have a feeling that I'll be hanging around this forum a lot for the next six months.
I recognize the first 3 properties but not the last. And I don't understand how each premise follows from one another but it's pretty cool that you can prove it with those very basic properties.
I'll...
D'oh... How did I miss that -__-;
Well, now that I know where 1 comes from lol, I still don't understand why the 1 is separated from the a if 1 IS a.
-a = (-1)a
-(a^2) = (-1) * (a^2)
Hey mark44 & vela just ignore that last part I wrote. It contains a whole bunch of extra and erroneous symbols because I was trying to figure out why – (a) = (-1) * (a)
I assumed that it was because -=(-1) which is where all the extra stuff came from. But it didn’t make sense to me when I...
This isn't really a homework problem but more of a clarification request. I'm studying prealgebra stuff right now and this rule kind of confused me.
-a^2 \neq (-a)^2 Ermmm...I typed out (-a)^2 but it's not showing.
I understand that the former produces a negative answer i.e. -2a while the...
This is such a good point. There's a reason why it's called spoon feeding. You're stuffing crap down my throat. My arms are flailing, I'm hyperventilating, I clearly don't want it! I absolutely hhhaatedd memorizing theorems and plugging them into solve mind numbingly repetitive, trivial...
Oh and thanks for suggesting "Introducing Mathematics". I will probably go out and buy it tomorrow. After I finish it I'll definitely lend it to my sister. She has this overpowering math phobia that holds her back in a lot of ways and I'm hoping this book will help her out. Like one of the...
For pre-algebra and algebra 1, I think no book beats "Algebra Survival Guide:a Conversational Guide for the Thoroughly Befuddled ".
https://www.amazon.com/dp/0965911381/?tag=pfamazon01-20
For basic geometry, "Geometry" by Harold Jacobs. Get an old edition, the first edition if you can...