## Aunt Pythia’s advice and a request for cool math books

First, my answer to last week’s question which you guys also answered:

*Aunt Pythia,*

*My loving, wonderful, caring boyfriend slurps his food. Not just soup — everything (even cereal!). Should I just deal with it, or say something? I think if I comment on it he’ll be offended, but I find it distracting during our meals together.*

*Food (Consumption) Critic*

——

You guys did well with answering the question, and I’d like to nominate the following for “most likely to actually make the problem go away”, from Richard:

I’d go with blunt but not particularly bothered – halfway through his next bowl of cereal, exclaim “Wow, you really slurp your food, don’t you?! I never noticed that before.”

But then again, who says we want this problem to go away? My firm belief is that every relationship needs to have an unimportant thing that bugs the participants. Sometimes it’s how high the toaster is set, sometimes it’s how the other person stacks the dishes in the dishwasher, but there’s always that thing. And it’s okay: if we didn’t have the thing we’d invent it. In fact having the thing prevents all sorts of other things from becoming incredible upsetting. My theory anyway.

So my advice to Food Consumption Critic is: don’t do anything! Cherish the slurping! Enjoy something this banal and inconsequential being your worst criticism of this lovely man.

Unless you’re like Liz, also a commenter from last week, who *left her husband because of the way he breathed*. If it’s driving you *that* nuts, you might want to go with Richard’s advice.

——

*Aunt Pythia,*

*Dear Aunt Pythia, I want to write to an advice column, but I don’t know whether or not to trust the advice I will receive. What do you recommend?*

*Perplexed in SoPo*

Dear PiSP,

I hear you, and you’re right to worry. Most people only ask things they kind of know the answer to, or to get validation that they’re not a total jerk, or to get permission to do something that’s kind of naughty. If the advice columnist tells them something they disagree with, they ignore it entirely anyway. It’s a total waste of time if you think about it.

However, if your question is super entertaining and kind of sexy, then I suggest you write in ASAP. That’s the very kind of question that columnists know how to answer in deep, meaningful and surprising ways.

Yours,

AP

——

*Aunt Pythia,*

*With global warming and hot summers do you think it’s too early to bring the toga back in style?*

*John Doe*

Dear John,

It’s *never* to early to wear sheets. Think about it: you get to wear the very same thing you sleep in. It’s like you’re a walking bed.

Auntie

——

*Aunt Pythia,*

*Is it unethical not to tell my dad I’m starting a business? I doubt he’d approve and I’m inclined to wait until it’s successful to tell him about it.*

*Angsty New Yorker*

Dear ANY,

Wait, what kind of business *is* this? Are we talking hedge fund or sex toy shop?

In either case, I don’t think you need to tell your parents anything about your life if you are older than 18 and don’t want to, it’s a rule of american families. Judging by my kids, this rule actually starts when they’re 11.

Of course it depends on your relationship with your father how easy that will be and what you’d miss out on by being honest, but the fear of his disapproval is, to me, a bad sign: you’re gonna have to be tough as nails to be a business owner, so get started by telling, not asking, your dad. Be prepared for him to object, and if he does, tell him he’ll get used to it with time.

Aunt Pythia

——

*Aunt Pythia,*

*I’m a philosophy grad school dropout turned programmer who hasn’t done math since high school. But I want to learn, partly for professional reasons but mainly out of curiosity. I recently bought *Proofs From the Book* but found that I lacked the requisite mathematical maturity to work through much of it. Where should I start? What should I read? (p.s. Thanks for the entertaining blog!)*

*Confused in Brooklyn*

Readers, this question is for you! I don’t know of too many good basic math books, so Confused in Brooklyn is counting on you. There have actually been lots of people asking similar questions, so you’d be helping them too. If I get enough good suggestions I’ll create a separate reading list for cool math page on mathbabe. Thanks in advance for your suggestions!

——

Please take a moment to ask me a question:

‘What Is Mathematics?’ by Courant & Robbins

“Numbers: Rational and Irrational” by Ivan Niven has some natural exposition of simple mathematical logic and arguments without getting bogged down in technical language and truth tables. It’s the first in the Anneli Lax New Mathematical Library series; some other books in that series would also be good choices.

Among the many great things about mathematics is slow aging. This book doesn’t cover a broad array of topics, but a programmer might find it interesting: Cantor’s “Contributions to the Founding of the Theory of Transfinite Numbers” (1915).

Contributions to the Founding of the Theory of Transfinite Numbers by Cantor,Georg. [1955] Paperback

Books are so 80’s. you need to get yourself onto the web and sign up for a free account on Kahn academy and jump in at the level you think you’re at and work up or down from there.

If you insist on a book, Jump Math has worked pretty well with my kids and has some good theoretical educational thought behind it.

Funny you should ask. My post about the top ten fun math books just appeared at the Nerdy Book Club site. I focused mostly on kids’ books. If you want something higher level, I loved

Surreal Numbers, and I just finished the delightfulJourney Through Genius: The Great Theorems of Mathematics, by William Dunham.For a very general quickie introduction to a number of math topics I think Steven Strogatz’s book from this year, “The Joy of X” is simply fabulous.

A slightly older volume, but still wonderful, is Keith Devlin’s “Mathematics: the New Golden Age.”

If the writer is looking for more textbook-like material I think the “….. For Dummies” series of math books are actually quite good, and there’s a ton of good (and free) instructional material on the Web as well.

Dated, sexist (although Sonya Kovalevskaya gets a chapter of her own), and E.T. Bell never, ever lets facts get in the way of a good story: Men of Mathematics.

Boy, was I inspired to become one! While still in grade school! Way out in the boondocks!

Rudy Rucker’s Mind Tools is an entertaining popular overview. He also has a delightful blog and writes great science fiction.

Mind Tools: The Five Levels of Mathematical Reality

Not a “fun” book necessarily, but if you would like a book that gently brings your level of mathematical maturity to the point where you can read “Proofs from the Book” with profit, I would suggest “Book of Proof” by Richard Hammack. It is available both as a real book and as a free pdf online.

“A Gentle Introduction to the Art of Mathematics” by Joseph Fields also looks nice for this purpose (I haven’t examined it as closely as “Book of Proof”).

the book “How to solve it- a structured approach” is quite useful for getting a feel for how proof-based mathematics is done. When you are feeling up for a challenge, Abbot’s “Understanding analysis” is quite a nice ‘handheld’ (at least, as much as can be done in this stage) book for what most people tend to think of as the most foundational of the subjects.

Introduction to Mathematical Thinking by Keith Devlin. It’s new, but this book got me from highschool to university relatively unscathed and focuses on real mathematics. I believe they have a Kindle version as well.

The Coursera course by Keith Devlin of Introduction to Mathematical Thinking.

I’m also from Brooklyn, and I was once a philosophy major, so obviously I’m the most qualified to give advice here:

I don’t know if it’s available for free online anymore, but the book we used at my school is “The Art of Proof” by Beck and Geoghegan. I thought it was very good, but you’re probably best off with the Coursera course, since it’s definitely free, and is, well, a course.

May I recommend anything by this gentleman?

http://faculty.tcu.edu/doran/Doranvita.htm

He was the best math teacher I ever had. He’s a functional analysis and operator algebra guy, which is very useful stuff — but he is really, really wonderful at explaining anything. That’s a completely different skill.

Here is an NPR segment on that Devlin course – sounds like it is directly up your alley. Also have a look at Paul Lockhart

MeasurementHarvard UP 2012.My friend Lynne loves

Mathematics: A Human Endeavor by Harold Jacobs

—–for a general reader, not a mathematician

I am not sure what “Confused in Brooklyn” is looking for, or

what constitutes a “cool math book.” That aside, here is

a short list of cool math books, for some value of “cool.”

Just about anything by Martin Garner, of course. One of the

collections of his Scientific American columns would be a

good starting point.

Hugo Steinhaus: “Mathematical Snapshots”

An oldie but a goodie.

James R. Newman: “Mathematics and the Imagination”

Another classic.

George Gamow: “One Two Three … Infinity”

Yet another classic. After writing about mathematics, Gamov

strays into science, but he can be forgiven.

Douglas Hofstadter: “Gödel, Escher, Bach: an Eternal Golden Braid”

’nuff said.

Ivars Peterson: “The Mathematical Tourist”

This and other more recent titles by Peterson give a layman’s

overview to different topics that can serve as departure points

for more in-depth and rigorous study. I believe that Ian Stewart

writes similar books, but I am unfamiliar with his work.

James R. Newman: The World of Mathematics

On the more serious side, this four volume set collects essays

on a wide range of topics.

G.H. Hardy: “A Mathematician’s Apology”

An excellent reflection on the mathematician’s point of view.

“A mathematician, like a painter or a poet, is a maker of

patterns. If his patterns are more permanent than theirs,

it is because they are made with ideas.” — G. H. Hardy

Hardy is a wonderful suggestion – it’s what gave me religion. The following two also deserve mention (the first is what led me to the second):

Davis and Hersh: “The Mathematical Experience”

Imre Lakatos: “Proofs and Refutations: The Logic of Mathematical Discovery”

Also, Confused in Brooklyn may want to attend a math circle. That was life-changing for me.

I looked here – https://www.mathcircles.org/Wiki_ExistingMathCirclePrograms – for a list of math circles. The NYC one sounds like it’s just for younger students and their teachers, but they may be worth contacting. Or maybe one of the others listed would work.