AKT-14/Homework Assignment 1 - Revision history

Frohlich: Stack arguments in the sum subscripts to increase readability.

2018-05-04T15:45:08Z

Stack arguments in the sum subscripts to increase readability.

← Older revision		Revision as of 11:45, 4 May 2018
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	<div align=center>		<div align=center>
	<math>\frac12\sum_{\text{xings }x\text{ between }\gamma_1\text{ and }\gamma_2}(-1)^x</math>		<math>\frac12\sum_{\scriptstyle\text{xings }x\text{ between}\atop\scriptstyle\gamma_1\text{ and }\gamma_2}(-1)^x</math>
	<math>= \sum_{\text{xings }x\text{ with }\gamma_1\text{ over }\gamma_2}(-1)^x</math>		<math>= \sum_{\scriptstyle\text{xings }x\text{ with}\atop\scriptstyle\gamma_1\text{ over }\gamma_2}(-1)^x</math>
	<math>= \sum_{\text{xings }x\text{ with }\gamma_2\text{ over }\gamma_1}(-1)^x</math>		<math>= \sum_{\scriptstyle\text{xings }x\text{ with}\atop\scriptstyle\gamma_2\text{ over }\gamma_1}(-1)^x</math>
	</div>		</div>

Drorbn at 14:45, 13 January 2014

2014-01-13T14:45:59Z

← Older revision		Revision as of 10:45, 13 January 2014
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	</div>		</div>

			'''Question 3.''' Use the techniques from Friday January 10, along with that Friday's handout ({{Pensieve link\|Classes/14-1350-AKT/FridayIntro.pdf\|the quantum pendulum}}), to write <math>U_t=e^{-itH}</math>, with <math>H=-\frac12\Delta+\frac12x^2</math>, in explicit terms, for <math>0<t<\frac{\pi}{2}</math>. Note that <math>U_t</math> interpolates between the identity and the Fourier transform.
	'''Question 2.'''

Drorbn at 14:36, 13 January 2014

2014-01-13T14:36:54Z

← Older revision		Revision as of 10:36, 13 January 2014
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	B. Prove that <math>\lambda(K)</math> is computable in polynomial time in the number of crossings of <math>K</math>.		B. Prove that <math>\lambda(K)</math> is computable in polynomial time in the number of crossings of <math>K</math>.

			'''Question 2.''' Using combinatorics alone prove that given a 2-component link diagram <math>D</math>, with components <math>\gamma_1</math> and <math>\gamma_2</math>,

			<div align=center>
			<math>\frac12\sum_{\text{xings }x\text{ between }\gamma_1\text{ and }\gamma_2}(-1)^x</math>
			<math>= \sum_{\text{xings }x\text{ with }\gamma_1\text{ over }\gamma_2}(-1)^x</math>
			<math>= \sum_{\text{xings }x\text{ with }\gamma_2\text{ over }\gamma_1}(-1)^x</math>
			</div>

			'''Question 2.'''

Drorbn at 14:26, 13 January 2014

2014-01-13T14:26:34Z

← Older revision		Revision as of 10:26, 13 January 2014
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	This assignment is due in class on Monday January 20. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the your readers will be having hard time deciphering your work they will give up and assume it is wrong.		This assignment is due in class on Monday January 20. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the your readers will be having hard time deciphering your work they will give up and assume it is wrong.

			This assignment was written on the HW session of Friday January 10. See {{BBS link\|AKT14-140110-191441.jpg}}, {{BBS link\|AKT14-140110-192041.jpg}}, and {{BBS link\|AKT14-140110-192042.jpg}}.

	'''Question 1.'''		'''Question 1.'''

			A. Prove that the set of all 3-colourings of a knot diagram is a vector space over <math>{\mathbb F}_3</math>. Hence <math>\lambda(K)</math> is always a power of 3.

			B. Prove that <math>\lambda(K)</math> is computable in polynomial time in the number of crossings of <math>K</math>.

Drorbn: Created page with "{{AKT-14/Navigation}} This assignment is due in class on Monday January 20. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right ..."

2014-01-05T15:40:57Z

Created page with "{{AKT-14/Navigation}} This assignment is due in class on Monday January 20. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right ..."

New page

{{AKT-14/Navigation}}

This assignment is due in class on Monday January 20. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the your readers will be having hard time deciphering your work they will give up and assume it is wrong.

'''Question 1.'''