Intereting Posts

Inductive proof of a formula for Fibonacci numbers
Can an algebraic variety be described as a category, in the same way as a group?
the sum of powers of $2$ between $2^0$ and $2^n$
A weak version of Markov-Kakutani fixed point theorem
Where can I learn more about the “else” operation / “else monoid”?
NFA from grammar productions
compound of gamma and exponential distribution
Why $\mathrm e^{\sqrt{27}\pi } $ is almost an integer?
order of “truncated” braid groups
Unconventional mathematics books
square cake with raisins
successful absurd formalities
Why is axiom of dependent choice necesary here? (noetherian space implies quasicompact)
What is the intuition for using definiteness to compare matrices?
Difference between the Jacobian matrix and the metric tensor

Are there any interesting books on math for children? Let’s break this into two questions: interesting books on math for children in elementary school and interesting books on math for children in middle school.

The only book I can think of that might work for kids is *The Little Schemer* by Friedman and Felleisen. To me, that seems almost as much a math book as a programming book.

And there’s also *Alice’s Adventures in Wonderland* and *Through the Looking Glass*, by Lewis Carroll, which, although they don’t really have any explicit math content in them, do have the sort of contradictory, paradoxical type of humor that many math people like.

- What are the theorems in mathematics which can be proved using completely different ideas?
- “Honest” introductory real analysis book
- Understanding measures on the space of measures (via examples)
- Historic proof of the area of a circle
- Did Zariski really define the Zariski topology on the prime spectrum of a ring?
- Pullbacks of categories

Also Raymond Smullyan’s books, but I think those might appeal mainly to older teens, but I’m not really sure.

Any ideas?

- Proof of Nesbitt's Inequality: $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge \frac{3}{2}$?
- What are power series used for? (a reference request)
- Geodesic equations and christoffel symbols
- Looking to understand the rationale for money denomination
- A question regarding Frobenius method in ODE
- What is the function $f(x)=x^x$ called? How do you integrate it?
- Intuition for gradient descent with Nesterov momentum
- Learning path to the proof of the Weil Conjectures and étale topology
- Complete classification of the groups for which converse of Lagrange's Theorem holds
- Find area bounded by two unequal chords and an arc in a disc

And there’s also Alice’s Adventures in Wonderland and Through the

Looking Glass, by Lewis Carroll, which, although they don’t really

have any explicit math content in them, do have the sort of

contradictory, paradoxical type of humor that many math people like (not the Pillow Problems, these are just problems, for older kids).

Actually Lewis Carroll does have more mathematically inclined children books like “A Tangled Tale” and “Pillow Problems”. And they share the humor we like (not Pillow Problems, these are just problems, for older children).

Especially I liked his own symbols for trigonometric functions. Detexify doesn’t seem to be able to find there LaTeX versions, so I’ve made an image:

As Lewis Carroll explains, this notion came from the “old trigonometry”, where sines and cosines were *real lines.* Seems it was not only Feynman who invented his own notion for them. I’ve read both books in Russian, where they were accompanied with his letters to children and his textbook “Symbolic Logic”. That was indeed a nice collection, I failed to find an English equivalent, but sure it should be somewhere.

I have not read it, but you could try “The Number Devil: A Mathematical Adventure”, by Hans Magnus Enzensberger.

I pored through this at least a couple times from 2^{nd} to 5^{th} grade:

Lots of illustrations; it looks at recreational-type math puzzles using a loose narrative structure with a cast of characters. It gave me some basic exposure to concepts in number theory (amicable numbers, perfect numbers), geometry (polygonal numbers, Möbius strips), logic (classic puzzles, the barber paradox), and combinatorics (permutations, combinations). And they don’t say so, but they do skirt around the Collatz conjecture, those *jerks*.

Use Amazon’s “look inside” feature to make sure it’s your style! This book is largely expository, rather than problem-solving, but it’s likely to get kids to look at a few concepts they haven’t encountered before.

I just found this book on Amazon: “Math Puzzles and Games, Grades 6-8: Over 300 Reproducible Puzzles that Teach Math and Problem Solving” by Terry Stickels.

It has a blurb by Martin Gardner on the back, so it’s probably quite good.

Also, *Flatland*. How could I forget *Flatland*?

Here is a link

http://mathcircle.berkeley.edu/

with lots to offer (not only) kids. There is a further link to a book section. Plus you might find a comparable endeavor near you, if it’s of interest.

- How can I learn to “read maths” at a University level?
- Let $T$ be a self-adjoint operator and$\langle T(w),w\rangle>0$ . If $\operatorname{dim}(W) = k$ then $T$, has at least $k$ positive eigenvalues
- Nilpotent groups are solvable
- How many trees in a forest?
- A stick of unit length is cut into three pieces of lengths $X, Y, Z$ according to its length in two sequence of cuts. Find Cov(X,Y).
- Consider the quadratic equation $ax^2-bx+c=0, a,b,c \in N. $ If the given equation has two distinct real root…
- The Ellipse Problem – finding an ellipse inside a triangle
- Classify groups of order 6 by analyzing the following three cases:
- Generating function of $a_{n}^2$ in terms of GF of $a_{n}$?
- Solution to differential equation $\left( 1-\lambda\frac{\partial}{\partial z}\right)w(x,y,z)-g(x,y,z+h)=0$
- algebra – matrices and polynoms
- Integral of bounded continuous function on $R$
- Is there an easy way to see associativity or non-associativity from an operation's table?
- Visualizing tuples $(a,b,x,y)$ of the extended Euclidean algorithm in a four-dimensional tesseract. Are there hidden symmetries?
- Find all $f(x)$ such that $f(gcd(x,y))=gcd(f(x),f(y))$