
Recent Posts
Archives
 March 2023
 January 2023
 May 2020
 April 2020
 March 2020
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: intermediate
Casual Introduction to Group Theory (3)
Subgroups [ This article approximately corresponds to chapter III of the group theory blog. ] Let G be a group under operation *. If H is a subset of G, we wish to turn H into a group by inheriting the operation from G. Clearly, … Continue reading
Posted in Notes
Tagged cyclic groups, generated groups, group theory applications, groups, intermediate, number theory, subgroups
Leave a comment
Casual Introduction to Group Theory (2)
Axioms of Group Theory [ This article approximately corresponds to chapter II of the earlier group theory blog. ] Group theory happens because mathematicians noticed that instead of looking at individual symmetries of an object, it’s far better to take … Continue reading
Posted in Notes
Tagged abelian groups, axioms, canonical maps, group orders, group products, group theory, intermediate, isomorphisms
Leave a comment
Combinatorial Game Theory Quiz 3
The quiz lasts 75 minutes and covers everything from lessons 112. For each of the following Nim games, find one good move for the first player, if any. (10 points) [ Note : exactly one of the games is a … Continue reading
Combinatorial Game Theory XII
Lesson 12 Recall the following Domineering configuration in lesson 10: The above game has a nice theory behind it. Definition : For any game G, the game –G (called miny–G) is defined to be: The game +G (called tiny–G) is defined … Continue reading
Posted in Notes
Tagged combinatorial game theory, computer science, domineering, game infinitesimals, impartial games, intermediate, minies, tinies, toads and frogs
1 Comment
Combinatorial Game Theory XI
Lesson 11 In this lesson, we will cover more on canonical forms. First recall that for m↑ + (*n) with m > 0, this game is positive except when (m, n) = (1, 1). Let’s consider the canonical forms of … Continue reading
Combinatorial Game Theory X
Lesson 10 In lesson 7, we learnt that if A, B are Left’s options in a game with A ≥ B, then we can drop B from the list of options and the game remains equal. In this lesson, we will … Continue reading
Combinatorial Game Theory Quiz 2
This quiz lasts 70 minutes and covers materials from lessons 19. Use the simplicity rule to compute the values of the following games. (10 points) {1/2  } {1/4  } {1/8  3/8} {0  7/8} {1/8  9/16} … Continue reading
Posted in Homework
Tagged combinatorial game theory, computer science, game numbers, intermediate, partial games, up game
Leave a comment
Combinatorial Game Theory IX
Lesson 9 Typically, at the end of a Domineering game, the board is divided into disjoint components, so the overall game is the (game) sum of the individual components. Suppose we have the following 6 components: How should the next … Continue reading
Combinatorial Game Theory VIII
Lesson 8 In this lesson, we will further familiarise ourselves with games involving numbers. At the end of the lesson, we will encounter our first positive infinitesimal: the “up” ↑. Here, an infinitesimal is a value which is strictly between –r and r … Continue reading
Combinatorial Game Theory VII
Lesson 7 [ Warning: another long post ahead. One of the proofs will also require mathematical induction. ] In this lesson, we will see how some games can be represented by numbers (which can be integers or fractions). We will also … Continue reading
Posted in Notes
Tagged combinatorial game theory, computer science, game numbers, hackenbush, intermediate, partial games, programming
Leave a comment