Suggested Math Syllabus for College-Bound Students - Teaching Math the Hungarian Way

Hungary has a long tradition of excellence in mathematics. Their approach is to present the students with problems that require patience and creativity to solve. Here are 21 problems that teach essential concepts in math. My next series of posts will discuss each problem below in detail. 

"It is enough to open minds; there is no need to overload them."

"Imagination is more important than knowledge." - The Notorious A. X. E. 

Topics Covered: algebra, geometry, trigonometry, calculus, statistics, probability

0. Proof That Dividing by Zero is Impossible

-concepts taught: inductive reasoning, asymptotes, fractions, limits

1. Proof of Pythagorean theorem with square inscribed in a square

-concepts taught: areas of squares and triangles, binomial expansion

2. Proof of the quadratic formula by completing the square on ax^2 + bx + c = 0

-concepts taught: order of operations, square roots

3. Gauss's Punishment

-concepts taught: arithmetic series and their sums

4. The Doubling Lily problem

-concepts taught: exponential growth, the logistic equation

5. Convert 60 MPH to feet per second

-concepts taught: dimensional analysis, unit conversion

6. Derivation of the power rule

-concepts taught: differential calculus

7. Proof that the square root of 2 is irrational

-concepts taught: proof by contradiction, order of operations

8. Proof that sin^2(x)+cos^2(x) = 1

-concepts taught: trigonometric functions, unit circle

9. The Hotdog-Hamburger problem

-concepts taught: linear programming, equation of a line

10. Mass of a pipe problem

-concepts taught: density, volume of a cylinder

11. The Dishonest Bartender problem

-concepts taught: material balances

12.  Derivation of the formula for conic volume

-concepts taught: solids of revolution, integral calculus

13. The rocket equation

-concepts taught: integral calculus, kinetic energy formula

14. The 5 card poker problem

-concepts taught: factorials, combinations

15. The fence problem

-concepts taught: 1st derivative test, area

16. The Boy-Girl problem

-concepts taught: tree diagrams, truth tables, binary logic

17. The IQ Bell Curve

-concepts taught: normal distribution, standard deviation

18. Pascal's Triangle

-concepts taught: binomial expansions, FOIL

19. The Futurama Problem AKA Fry's Bank Account

-concepts taught: compound interest, exponential growth, the rule of 72

20. Euler's formula and identity

-concepts taught: complex numbers, polar coordinates