Categories
- Book & Article Reviews (3)
- Education (8)
- Mathematics (72)
- Algebra (6)
- Calculus (10)
- Combinatorics (26)
- Foundations (4)
- Games (7)
- Geometry (11)
- Logic (9)
- Probability (6)
- Ramsey Theory (3)
- Set Theory (8)
- Topology (11)
- Wednesday Problem (40)
- Meta (15)
- Philosophy (15)
- Popular (7)
- Recreation (35)
Search Walks on Mind
Like this blog?
- New webpage at www.vadimkulikov.org March 24, 2017
- (Ir)rational Behavior of Calculation October 18, 2011
- The Product of Topological Spaces Does Not Obey Cancellation October 12, 2011
- Wild Embeddings October 11, 2011
- Progress October 4, 2011
- Class-metric August 24, 2011
- Intellectual Lazyness August 22, 2011
- Time Limit: One Minute! August 17, 2011
- Douglas Hofstadter: I Am a Strange Loop. August 15, 2011
- 0.999999……=1? (continuation) July 10, 2011
- Walks on Planets July 5, 2011
- 0.999999….. = 1? July 3, 2011
- Prisoners’ problem 6 June 29, 2011
- I am back! June 28, 2011
- A non-associative “group” March 21, 2011
- Why I haven’t blogged March 21, 2011
- Doodling with Fractals and Persistent Worms. January 2, 2011
- Five groups November 23, 2010
- Splitting A Rectangle November 17, 2010
- Sphere November 10, 2010
Tags
Archives
- March 2017 (1)
- October 2011 (4)
- August 2011 (4)
- July 2011 (3)
- June 2011 (2)
- March 2011 (2)
- January 2011 (1)
- November 2010 (5)
- October 2010 (6)
- July 2010 (4)
- June 2010 (4)
- May 2010 (2)
- April 2010 (5)
- March 2010 (11)
- February 2010 (7)
- January 2010 (10)
- December 2009 (11)
- November 2009 (7)
Category Archives: Algebra
(Ir)rational Behavior of Calculation
We had the following set of exercises with a group of secondary school students (in Ressun lukio). Assume that a and b are positive real numbers. Then assume one of the following: (i) a and b are both rational (ii) … Continue reading
Posted in Algebra, Calculus, Education, Mathematics, Wednesday Problem
1 Comment
A non-associative “group”
Here is what I’ve been doing for the past hour: proving that associativity does not follow from other group axioms including that the left and right inverses are the same and the neutral element is unique. Let us define the … Continue reading
Posted in Algebra, Mathematics
1 Comment
A Year Problem
There are more year problems than years. But since I have been pondering on this particular one, I will present it here. You are allowed to use +, -, / and * (plus, minus, division and multiplication) signs and bracketing. … Continue reading
Posted in Algebra, Combinatorics, Mathematics, Recreation, Wednesday Problem
12 Comments
Using Abstract Algebra To Understand Basic Combinatorics
Pascal’s triangle has many fascinating properties. One of them is for any given prime number p, the number of k-element subsets (0< k < p) of a p-element set is divisible by p: [tex]p | \binom{p}{k}\qquad \qquad \qquad (*)[/tex] You … Continue reading
Euler’s Riddle
Please comment your solutions, questions and remarks.. I found in a recreational book the following riddle attributed to Leonard Euler. The book gives a clumsy solution involving solutions of quadratic equations, a lot of fractions and half a page of … Continue reading
Posted in Algebra, Mathematics, Recreation, Wednesday Problem
2 Comments
How Many Good Colorings?
Please comment your solutions, questions and remarks.. Suppose G is a graph in which each vertex has three neighbours, for example: Suppose we have three colors, red green and blue, with which we want to color the edges of the … Continue reading
Posted in Algebra, Combinatorics, Mathematics, Wednesday Problem
Leave a comment