User Isaac

72 votes

10 answers

40k views

Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$

asked Jul 23, 2010 at 4:05

58 votes

12 answers

71k views

Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $

sequences-and-series analysis convergence-divergence logarithms closed-form

asked Jul 26, 2010 at 8:38

45 votes

7 answers

3k views

Bad Fraction Reduction That Actually Works

elementary-number-theory arithmetic fractions fake-proofs

asked Jul 5, 2011 at 18:27

34 votes

11 answers

14k views

Mandelbrot-like sets for functions other than $f(z)=z^2+c$?

fractals dynamical-systems

asked Jul 29, 2010 at 2:57

32 votes

2 answers

15k views

Probability that a stick randomly broken in two places can form a triangle

probability monte-carlo

asked Jul 25, 2010 at 5:31

25 votes

15 answers

7k views

Useful examples of pathological functions

soft-question big-list calculus real-analysis

asked Jul 26, 2010 at 21:35

22 votes

2 answers

8k views

Circular permutations with indistinguishable objects

combinatorics

asked Jul 23, 2010 at 18:14

21 votes

3 answers

2k views

Birthday-coverage problem

probability coupon-collector

asked Mar 13, 2011 at 20:13

20 votes

2 answers

4k views

What is the best way to solve an equation involving multiple absolute values?

algebra-precalculus faq

asked Aug 23, 2010 at 22:00

19 votes

1 answer

169k views

Solving Triangles (finding missing sides/angles given 3 sides/angles)

geometry algebra-precalculus trigonometry euclidean-geometry triangles

asked Feb 7, 2012 at 3:31

15 votes

4 answers

11k views

Is "locally linear" an appropriate description of a differentiable function?

calculus education

asked Oct 21, 2010 at 19:11

14 votes

1 answer

2k views

What is the standard interpretation of order of operations for the basic arithmetic operations?

algebra-precalculus arithmetic faq

asked May 1, 2011 at 20:35

11 votes

4 answers

873 views

Describe the locus in the complex plane of the zeros of a quartic polynomial as the constant term varies

algebra-precalculus polynomials roots quartics

asked Jul 23, 2010 at 3:59

6 votes

5 answers

2k views

Least wasteful use of stamps to achieve a given postage

combinatorics optimization algorithms contest-math

asked Jul 26, 2010 at 21:48

6 votes

5 answers

3k views

Usefulness of Conic Sections

algebra-precalculus conic-sections education

asked Jul 28, 2010 at 18:36

5 votes

3 answers

2k views

How to determine arc measures from angles between secant and tangents (without trigonometry)

geometry trigonometry euclidean-geometry circles

asked Dec 8, 2010 at 3:03

5 votes

1 answer

3k views

Proving the Shoelace Method at the Precalculus Level

geometry algebra-precalculus contest-math analytic-geometry

asked Jul 28, 2010 at 18:26

5 votes

4 answers

1k views

What transformations of the plane are geometrically constructable (compass & straight edge)?

geometry euclidean-geometry geometric-construction transformational-geometry

asked Jul 23, 2010 at 18:40

5 votes

6 answers

3k views

Why, conceptually, do limaçons $r=a+b\cos\theta$ have dimples when $|\frac{a}{b}|<2$?

geometry intuition analytic-geometry plane-curves polar-coordinates

asked Oct 9, 2011 at 17:49

2 votes

1 answer

158 views

Solving inequalities comparing $f(x)$ to $0$ where $f$ is an elementary function

algebra-precalculus inequality

asked May 1, 2011 at 20:19

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20 Questions

Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$

Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $

Bad Fraction Reduction That Actually Works

Mandelbrot-like sets for functions other than $f(z)=z^2+c$?

Probability that a stick randomly broken in two places can form a triangle

Useful examples of pathological functions

Circular permutations with indistinguishable objects

Birthday-coverage problem

What is the best way to solve an equation involving multiple absolute values?

Solving Triangles (finding missing sides/angles given 3 sides/angles)

Is "locally linear" an appropriate description of a differentiable function?

What is the standard interpretation of order of operations for the basic arithmetic operations?

Describe the locus in the complex plane of the zeros of a quartic polynomial as the constant term varies

Least wasteful use of stamps to achieve a given postage

Usefulness of Conic Sections

How to determine arc measures from angles between secant and tangents (without trigonometry)

Proving the Shoelace Method at the Precalculus Level

What transformations of the plane are geometrically constructable (compass & straight edge)?

Why, conceptually, do limaçons $r=a+b\cos\theta$ have dimples when $|\frac{a}{b}|<2$?

Solving inequalities comparing $f(x)$ to $0$ where $f$ is an elementary function