I got an email this afternoon from a reader who is interested in learning mathematics — as an adult, post-college. The reader has an advanced degree in a humanities discipline and never studied mathematics, but recently he’s become interested in learning and is looking for a place to start.

I recommended The Mathematical Experience by Davis and Hirsch, How to Solve It by Polya, and any good college-level textbook in geometry (like Greenberg, or for a humanities person perhaps Henderson). I felt like these three books give an ample and accessible start at — respectively — the big picture and history of the discipline, the methodology of mathematicians, and a first step into actual mathematical content.

But what I thought this was an interesting question, and I wonder if the other readers out there would have similar suggestions for books, articles, movies or documentaries… anything that would be of use to an educated adult learner with little math background but a lot of genuine interest. Leave your suggestions in the comments.

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I guess it could be called “recreational math”, but I like Isaac Asimov’s book, Asimov on Numbers. It does a good job explaining pi, e, and i (among other math concepts) in layman’s terms, along with bio sketches of greats like Euler, Gauss, Leibnitz, and Newton. It’s out of print, but my library had it, and I bought a copy used on Asimov for not much money.

Books that inspired me to want to read more were William Dunham’s Journey Through Genius, The Great Theorems of Mathematics. I didn’t know enough math to make it entirely through the book but the first few chapters alone were fascinating enough to make the entire book worth it. It was my first introduction to proof beyond the token gesture that I got in tenth grade geometry.

Euclid’s Window : The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow

The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics by Marcus Du Sautoy

I am in the middle of reading “A Certain Ambiguity” which is a fictional math novel. I’m on about page 50 and it’s outrageously good. Right now the author has (intentionally) thrown out the problem that an infinite sequence can not be treated under the same rules as a finite sequence, has shown how things can go wrong if you do, but hasn’t said what the solution to this problem is. So, these kinds math problems come up and are discussed philosophically rather than via “memorize the rules and apply” , meanwhile the plot, if you will, involves two characters philosophically discussing and trying to apply “rigor” to faith and God. (Yet another discussion of faith vs. reason is not that interesting at all to me, I just like the math problems in the book and watching how each of the characters in the books tackles the same problem in different ways)

Now that I am an adult and don’t have to be held to the time constraints of a course I learn at a leisurely pace. Gelfand’s Algebra was a good starting place to review elementary algebra. In fact, there was enough of demand on the part of other liberal arts folks to warrant creating a solutions manual and putting it up online, the link is on my blog. The problems are not all so easily solved so do not be disheartened when you come across a tough one.

Beckenbach’s Introduction to Inequalities has been a lot of fun as well, I haven’t finished it. Who knew that there were so many different ways of defining absolute value? I only work that one on Saturdays when I have a lot of time.

Serge Lang’s “Basic Math” just came to me in the mail and looks promising. Lang was a Bourbaki and his book is a review of everything one ought to know before taking Calculus. The writing style is as terse as can be imagined and there are plenty of proofs.

Another option for your friend are the Art of Problem Solving books. They don’t offer as much of a structured approach to math as I personally am interested in but some of the problems are interesting and the books themselves are available through the public libraries and so can be reviewed before buying them.

I have no shortage of books to tackle, what I lack is time: Also on my list of “to do” are SI Gelfand’s Sequences, Combinations, and Limits and Kiselev’s Geometry (Alexander Givental at www. Sumizdat.org for sample pages), I also have several of the titles from: https://www.maa.org/ecomtpro/Timssnet/books/NML.cfm that look great such as Niven’s Numbers Rational and Irrational, Topology (may be more like toplogy appreciation than topology but it goes well with Donal OShea’s book “The Poincare Conjecture” Oystein’s Ore’s Number Theory pairs well with Paul Hoffman’s “The Man Who Only Loved Numbers” which is strictly speaking a biography of Erdos and neither math nor math history.

If one wants to have fun considering interesting problems my advice is to stay away from college textbooks. The thing that has surprised me the most is how very different the kinds of math problems are from these books and the ones that I have found the most enjoyable. In a college text the problems in the exercises are meant to be solved within minutes, but in these other books it’s possible to spend a day or two thinking about a single problem before the solution occurs to you…or not.

So I would recommend Harold Jacob’s Mathematics A Human Endeavor. Its a great survey course of interesting topics mostly geared toward traditional learnings. Another great text book like book is Peter Tannenbaum’s Excursions in Modern Mathematics, it is highly readable and contains interesting topics like voting theory and fractals. A Calculus book might also be a reasonable choice I would suggest the one by Deborah Hughes Hallett. Finally, if they would rather read about math Martin Gardner’s books are always great. Devlin’s Mathematics The New Golden Age is also good. With a humanities interest they might also really get into Godel Escher Back.

Perhaps some of these might help.

Here at the University of Canterbury, New Zealand, I recently held a poll of my fellow mathematicians, asking them first to nominate, then to vote for their favourite maths book suitable for introducing a freshman to mathematical culture. Voters were asked for their top three picks, with number one garnering three points, number two getting two points, and number three just one point. The full list, and tally of points is:

“Fermat’s Last Theorem” by S Singh – 9 points

“The problems of Mathematics” by I Stewart – 7 points

“What is Mathematics” by Courant & Robbins – 4 points

“How to Solve it” by Polya – 4 points

“A Beautiful Mind” by S Nasar – 3 points

“Mathematicians’ Delight” by WW Sawyer – 3 points

“The Pleasures of Counting” by TW Korner – 3 points

“Art of Computer Programming vol 1” by Knuth – 3 points

“The Colossal Book of Mathematics” by M Gardner – 3 points

“Surely You’re Joking, Mr Feynman” by R Feynman – 2 points

“The Parrot’s Theorem” by D Guedj – 2 points

“Five Golden Rules” by JL Casti – 2 points

“A Tour of the Calculus” by D Berlinski – 2 points

“The History of Mathematics” by Katz – 2 points

“Art of Computer Programming vol 2” by Knuth – 2 points

“Preulde to Mathematics” by WW Sawyer – 2 points

“Mathematical Gems” by Honsberger – 2 points

“Godel, Escher, Bach” by D Hofstadter – 1 point

“Mathematical Plums” by Honsberger – 1 point

“Nonplussed!” by J Havil – 1 point

“Art of Computer Programming vol 3” by Knuth – 1 point

“The Music of the Primes” by M du Sautoy – 1 point

I was very happy that Singh’s “Fermat’s Last Theorem” won, because this was the book (and documentary) which first made me think about a career in mathematics. It takes a particular puzzle, and uses it to introduce concepts, personalities, stories, and the general culture of mathematics.

Martin Gardner’s collections of Mathematical Games columns from Scientific American are great fun. The entire collection is available on CD-ROM now, too, if you like the whole pdf thing.

Jan Gullberg’s “Mathematics: From the Birth of Numbers” is an interesting book.

Back in the day, what got me interested in maths (having previously been heading in the direction of physics) was James Gleick’s book “Chaos”.

For something a bit more heavy-duty: Roger Penrose’s “Emperor’s New Mind” or (if you’re feeling

reallysadistic) “The Road to Reality”.I second “Fermat’s Last Theorem” as a good read.

Basically anything that explains Cantor’s diagonalisation proof in a comprehensible way. If they don’t find that the most ingenious and amazing thing they’ve ever read, they’ll never like anything in maths. š

I checked out the two Geometry books you recommended. They are a bit expensive ($106 new, and $81 used for the first one, and $71 new/$41 used for the second one). Is there any other good, simple geometry book (for someone who never had it in high school, but is interested in learning) should start with? I really appreciate this post.

Margot

Pingback: Another request for introductions to math « Casting Out Nines

I am in this camp, admitted here: http://tinyurl.com/imre-lakatos-proofs

So, thanks for the reference in the post and comments.

What do you think of Keith Devlin’s “The Language of Mathematics?”

Not looking for compliment as I loved it and still will, but curious to hear the take of someone familiar with the topic. This book is not math learning as much as an introduction to multiple disciplines and the relationships between them.

So, from that perspective…?