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

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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

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Combinatorial Game Theory Quiz 3

The quiz lasts 75 minutes and covers everything from lessons 1-12. 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

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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

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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

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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

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Combinatorial Game Theory Quiz 2

This quiz lasts 70 minutes and covers materials from lessons 1-9. 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

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