Math Affinity Puzzles

Part 1: Precalculus

1. Integers : Rational Numbers
2. Circle : Center and Radius
3. 3 − √7 : 3 1√7 [see book for full equation in title]
4. y = logb x : x = by
5. Even-Degree Polynomial : Horizontal Line Test
6. Nonorigin Point in the Plane : Polar Coordinates (r, θ ) with 0 ≤ θ < 2π
7. am : am−n [see book for full equation in title]
8. x = 0 : log10 x [see book for full equation in title]
9. Degree of a Polynomial : Number of Real Roots
10. ex : ln x
11. Complex Numbers : Real Numbers
12. x2+1 : x = 1 [see book for full equation in title]
13. y = arctan(x) + 3 : y = arctan(x)
14. √ab : √a√b
15. Positive Integers : Prime Numbers and Composite Numbers
16. Polynomial Function : Asymptote
17. x2 = x : x = 1
18. Circle : Ellipse
19. (A ∩ B) ∪ (A ∩ C) : A ∪ (B ∩ C)
20. log2 x : ln x
21. tan x : cot x
22. Function : Symmetric about the x-axis

Part 2: Calculus

23. Rolle’s Theorem : Mean Value Theorem
24. y = cos x : y − 1 = √3− 2 (x − π ) [see book for full equation in title]
25. Riemann Sum : Definite Integral
26. Critical Point : Local Extremum
27. limx→π sin x : sin x
28. Marginal Cost : Total Cost
29. limx→0 cos x : L’Hôpital’s Rule
30. Differentiable : Continuous
31. Maclaurin Series : Taylor Series
32. Concave-Up Function : Minimum
33. Definite Integral : Area
34. Factorials : Polynomials
35. Addition : Arithmetic Sequence
36. 1 : ln x [see book for full equation in title]
37. Velocity : Position
38. Taylor Polynomials : Smooth Function
39. Chain Rule : Integration by u-substitution
40. Improper Integral : Definite Integrals
41. Everywhere-Zero Derivative : Differentiable Function
42. f (xx) −f (a) : f ′(a) [see book for full equation in title]
43. ∞ 3 2 n : 3 [see book for full equation in title]
44. Intermediate Value Theorem : |x| on the Interval [−2, 1]

Part 3: Postcalculus

45. Dot Product : Orthogonal Vectors
46. □□2f [see book for full equation in title]
47. Gradient : Level Curve
48. □□2f □□2f − а □□2f [see book for full equation in title]
49. Three Distinct Points : Plane in R3
50. Gradient : Directional Derivative
51. Concavity : Euler’s Method
52. Separation of Variables : Homogeneous Differential Equation
53. Switching Two Rows : Determinant
54. Matrix : Reduced Row Echelon Form
55. Eigenvalue : Eigenvector
56. Determinant : Rank
57. Matrix Multiplication : Square Matrices
58. Permutations : Determinant
59. Event : Sample Space
60. Successive, Independent Coin Flips : Probability of Heads
61. Cumulative Distribution Function : Probability Density Function
62. Geometric Distribution : Exponential Distribution
63. Eulerian Path : Graph
64. Tree : Cycle
65. Bipartite Graph : Three-Colorable
66. Planar Graph : K5 Subgraph

Biography

Katie Ballentine is a software engineer at Guild Education. Previously, she was director of communications at Mathematical Sciences Publishers (MSP), and before that, she was a mathematical copy editor at MSP and Mathematical Reviews. She has taught a variety of undergraduate math classes.

Michael A. Jones is an associate editor at the American Mathematical Society’s Mathematical Reviews. He was a faculty member for 14 years, including as an associate professor in mathematics at Montclair State University, NJ. He served as editor of the Mathematical Association of America’s Mathematics Magazine from 2014 to 2019. In the summers, he teaches high school students through the University of Michigan’s Michigan Mathematics and Science Scholars program.

Lon Mitchell is currently an associate professor of mathematics at Eastern Michigan University, was previously an editor for the American Mathematical Society, and has taught for multiple, gifted, high-school enrichment programs, including for the University of Michigan.

Jennifer M. Wilson is an associate professor of mathematics at The New School, where she has been a faculty member since 2003. She has taught most of the standard courses in the undergraduate mathematics curriculum and has published research in a variety of different journals, including Mathematics of Social Sciences, Mathematical Methods of Operations Research, the College Mathematics Journal, and Mathematics Magazine.