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UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics Homework February 6, 2008 John Baez homework by Brian Rolle The Euclidean Group 4. Suppose that f : Rn Rn is a map that preserves distances: |f (x) f (y)| = |x y| for all x, y Rn . Then f (x) = Rx + u for some (R, u) E(n). |...
UC Riverside >> PHYS >> 291 (Fall, 2008)
A Spring in Imaginary Time Erin P. J. Pearse 1. Suppose you have a spring in Rn with xed endpoints, tracing out a curve q : [s0 , s1 ] Rn , n q(s0 ) = a, q(s1 ) = b. If the spring is in a potential V R R, what curve will the spring trace out when...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Action as a Functor Questions by: John C. Baez, October 4, 2004 Answers by: Toby Bartels1 , 2004 October 14 In class I said some mysterious things about how the electromagnetic eld is a U(1) connection on spacetime, while the Feynman path integral i...
UC Riverside >> PHYS >> 291 (Fall, 2008)
INSTITUTE OF PHYSICS PUBLISHING Nonlinearity 17 (2004) 15711606 NONLINEARITY PII: S0951-7715(04)67794-2 Connecting orbits and invariant manifolds in the spatial restricted three-body problem G G mez1 , W S Koon2,5 , M W Lo3 , J E Marsden2 , J Masde...
UC Riverside >> PHYS >> 291 (Fall, 2008)
A Brief History of Time John C. Baez, September 23, 2004 Note: all gures are approximate! Working Backwards from Now 60 years ago Invention of the computer. 130 years ago Invention of the telephone. 180 years ago Fossil fuel revolution: coal, tra...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
Action as a functor Miguel Carrin Alvarez o 2004 October 14 1. Connections as functors. The functor S must map : p q to S(): S(p) S(q), where S(p) and S(q) are objects in R. But R is a category with one object only, so S(p) = S(q) = and the functo...
UC Riverside >> PHYS >> 291 (Fall, 2008)
m ! ! 1 Ua#8Xg@1 {0 p pv1 E31 USo v\' v1 a |s# \'1 o#d8rpv{dr \' Q y\' pp p# cUSv j m y 1 ! 1 1 1 ! 1 l eAc`bex2#ede2Q032|X2edcaY@8i3D2c2t0xF cQDsUhS|caQ33D8Y3tYth t ez b ~ b A H b A F H T` f b ` CG H...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics March 11, 2008 John Baez Homework by: Scot Childress The LaplaceLungeRenz Vector Let q denote the dierence in position of two particles in R3 , |q| the magnitude of q, and m the reduced mass. Supposing that the particles exert an...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
Categorifying Fundamental Physics John Baez Despite the incredible progress over most of the 20th century, and a continuing ow of new observational discoveries neutrino oscillations, dark matter, dark energy, and evidence for ination theoretical re...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Stanford Department of Mathematics Colloquium HIGHER GAUGE THEORY JOHN BAEZ University of California at Riverside Abstract Gauge theory describes the parallel transport of point particles using the formalism of connections on bundles. In both strin...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Groupoidication Made Easy John C. Baez, Alexander E. Honung, and Christopher D. Walker Department of Mathematics, University of California Riverside, CA 92521 USA December 30, 2008 Abstract Groupoidication is a form of categorication in which vector ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
UNIVERSITY OF CALIFORNIA RIVERSIDE Lie 2-Algebras A Dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Mathematics by Alissa Susan Crans August 2004 Dissertation Committee: Professor John B...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Higher Categories, Higher Gauge Theory II John C. Baez joint work with: Toby Bartels, Alissa Crans, James Dolan, Aaron Lauda, Urs Schreiber, Danny Stevenson. Unni Namboodiri Lectures April 10th, 2006 x hol() & 8 y hol() hol() $ : Not...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Being an Octopus1 John C. Baez, April 27, 2004 In their book Combinatorial Species and Tree-Like Structures, Bergeron, Labelle and Leroux discuss a structure type Oct, called being an octopus. Instead of dening it, Id like you to guess it from some ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
UNIVERSITY OF CALIFORNIA, SANTA CRUZ AS/SCP/1405-1 COMMITTEE ON THE LIBRARY Resolution on Ties with Elsevier Journals To the Academic Senate, Santa Cruz Division: Facing a challenge to scholarly communication The University of California system fac...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics Homework February 21, 2008 John Baez Angular Momentum and Rotations In this problem we will see that angular momentum generates rotations for a particle in R n . We begin by recalling a bit about rotations. Let O(n) be the orthog...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
Derek Wise October 7, 2004 Quantum Gravity Seminar HW #1 Groups as Categories In what follows, by group I always mean a group in the categorical sense: A group is a groupoid with one object. I use the traditional backward order of composition: f g m...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics, Lecture 13 February 21, 2008 lecture by John Baez notes by Alex Honung 1 Lie Algebras Lie groups are groups that are also manifolds. These let us describe continuous symmetries in physics. A classic example is SO(n) - the grou...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics Homework February 7, 2008 John Baez This homework gives you some choice in which problems you do, depending on how ambitious you feel. In the section on the Euclidean group you can either do problems 13, or if youre feeling more ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
A Spring in Imaginary Time QG Homework 2 Fall 2006 Alex Honung October 18, 2006 One of the stranger aspects of Lagrangian dynamics is how it turns into statics when we replace the time coordinate t by it - or in the jargon of physicists, when we Wick...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Quantum Quandaries: A Category-Theoretic Perspective John C. Baez Department of Mathematics, University of California Riverside, California 92521 USA email: baez@math.ucr.edu April 7, 2004 To appear in Structural Foundations of Quantum Gravity, eds. ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Physics and analysis on noncompact manifolds1 Miguel Carrin Alvarez2 o Department of Mathematics University of California Riverside, CA 92521, USA miguel@math.ucr.edu November 5, 2004 1 2 UCR Math department geometry seminar, November 5, 2004 Joint...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Math 260: Perturbation theory Miguel Carrin Alvarez o 1. The perturbation series. Starting with t tn t2 (t) = n0 0 0 0 ei(ttn )H0 (iV )ei(tn tn1 )H0 ei(t2 t1 )H0 (iV )eit1 H0 dt1 dtn1 dtn we get t tn1 t2 t (t) = n1 0 0 t tn 0 (iV )ei(t...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Higher dimensional word problems with applications to equational logic Albert Burroni Universit PARIS 7, UFR de maths e 2 place Jussieu, 75005 Paris The word problem on a monoid admits two natural generalizations: The rst one is the extension from ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
Garett M. Leskowitz 2429 Pierce Hall Deparment of Chemistry University of California Riverside, CA 92521 (909) 787-7365 Current Position Education 1790 West Arrow Route #202 Upland , CA 91786 (909) 981-6709 garett@citrus.ucr.edu Postdoctoral Resear...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics, Lecture 5 January 24, 2008 lecture by John Baez notes by Alex Honung 1 Symmetries and Conserved Quantities the n-Body Problem Today we will begin our quest to see where symmetries come from. For this, let us talk about symmet...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
The Kepler Problem Math 241 Homework John Baez The goal of this problem is to see why two particles interacting via gravity move along nice curves like ellipses, parabolas and hyperbolas. This is called the Kepler problem since it was Kepler who dis...
UC Riverside >> PHYS >> 291 (Fall, 2008)
The Classifying Space of a Topological 2-Group John C. Baez Danny Stevenson June 6, 2008 Abstract Categorifying the concept of topological group, one obtains the notion of a topological 2-group. This in turn allows a theory of principal 2-bundles ge...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Connections as Functors John C. Baez, October 21, 2004 In this homework well see how a vector bundle E equipped with a connection over a manifold X gives a functor F : P(X) Vect where P(X) is the category of paths in X, dened in the last homework. ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
Math 260: Categorifying the Riemann Zeta Function Miguel Carrin Alvarez o 1. Subcategories have faithful inclusions. Assume that C is a subcategory of D, that is, there is a functor i: C D which is an inclusion of objects and morphisms, preserving u...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
The Euclidean Group, the Galilei Group and the Free Particle Math 241 Homework John Baez This homework gives you some choice in which problems you do, depending on how ambitious you feel. In the section on the Euclidean group you can either do prob...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> PHYS >> 291 (Fall, 2008)
COURSE NOTES ON QUANTIZATION AND COHOMOLOGY, WINTER 2007 JOHN BAEZ NOTES BY APOORVA KHARE FIGURES BY CHRISTINE DANTAS DEPARTMENT OF MATHEMATICS, UNIVERSITY OF CALIFORNIA RIVERSIDE, CA 92521, USA Contents 1. Preface 3 4 4 6 8 8 9 11 11 11 13 14 14 1...
UC Riverside >> PHYS >> 291 (Fall, 2008)
StreetFest Categories in Algebra Geometry and Mathematical Physics Conference in honour of Ross Street\'s 60th birthday July 11-16 2005 Macquarie University, Sydney http:/streetfest.maths.mq.edu.au Participants* Nils Baas John Baez Michael Batanin Cl...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics Homework January 17, 2008 John Baez homework by John Huerta Homework 1 Solve Newtons second law F = ma for q(t) R3 for F (t) = (0, 0, mg), the force felt by a particle near the Earths surface only under the inuence of gravity. F...
UC Riverside >> PHYS >> 291 (Fall, 2008)
From Loop Groups To 2-Groups John C. Baez Joint work with: Aaron Lauda Alissa Crans Danny Stevenson & Urs Schreiber 1 G f1 D +3 f2 More details at: http:/math.ucr.edu/home/baez/2group/ 1 Higher Gauge Theory Ordinary gauge theory describes h...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Physics, Topology, Logic and Computation: A Rosetta Stone John C. Baez Department of Mathematics, University of California Riverside, California 92521, USA Mike Stay Google, 1600 Amphitheatre Pkwy Mountain View, California 94043, USA email: baez@math...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Some Denitions Everyone Should Know John C. Baez, July 6, 2004 A topological quantum eld theory is a symmetric monoidal functor Z: nCob Vect. To know what this means, we need some denitions from category theory. These make for rather dry reading un...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics, Lecture 10 February 12, 2008 lecture by John Baez notes by Alex Honung 1 How Observables Generate Symmetries Hamiltons equations are rst-order dierential equations. In the language of dierential geometry, they are all about a ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
Classical Mechanics, Lecture 17 March 6, 2008 lecture by John Baez notes by Alex Honung 1 Weakly Hamiltonian Group Actions (q, p). We worked out the The phase space for the free particle in Rn is X = T Rn Rn Rn = action of the Galilei group on ...
UC Riverside >> PHYS >> 291 (Fall, 2008)
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UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 2 P2.1* P2.4* (a) Req = 25 (b) Req = 25 The 2- and 4- resistances are in parallel having an equivalent resistance of 1.333 . Similarly, the 1- and 3- resistances are in parallel and have an equivalent resistance of 0.75 . Finally, t...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 8 P12.3* 1 K = 2 KP (W / L) = 0.25 mA/V 2 (a) Saturation because we have vGS Vto and vDS vGS - Vto. iD = K(vGS - Vto)2 = 2.25 mA (b) Triode because we have vDS < vGS - Vto and vGS Vto. iD = K[2(vGS - Vto)vDS - vDS2] = 2 mA (c) Cutoff...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 4 P3.5* i =C dv dt dv i 100 10 6 = = 0.05 V/s dt C 2000 10 6 v 100 t = = = 2000 s dv dt 0.05 P3.7* i (t ) = C = 10 5 d (100 sin 1000t ) dt = cos(1000t ) dv dt p (t ) = v (t )i (t ) = 100 cos(1000t ) sin(1000t ) = 50 sin(2000t ) ...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 6 P5.41* This is a capacitive load because the reactance is negative. 2 P = I rms R = (15) 2 100 = 22.5 kW 2 Q = I rms X = (15) 2 ( 50) = 11.25 kVAR Q = tan 1 = tan 1 ( 0.5) = 26.57 P power factor = cos( ) = 89.44% P5.44* I= 1000 20 ...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 1 P1.4* The reference direction for iab points from a to b. Because iab has a negative value, the current is equivalent to positive charge moving opposite to the reference direction. Finally since electrons have negative charge, they are m...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 3 P2.27* v = 0.1 mA Rw = 50 mV Rg = P2.29* 50 mV = 25 m 2 A 0.1 mA Combining R2 and R3 , we have an equivalent resistance 1 Req = = 10 . Then using the voltage-division principle, we have 1 R2 + 1 R3 v= Req 10 v s = 10 = 3.333 V ...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 2 P2.1* P2.7* (a) Req = 25 (b) Req = 25 The 2- and 4- resistances are in parallel having an equivalent resistance of 1.333 . Similarly, the 1- and 3- resistances are in parallel and have an equivalent resistance of 0.75 . Finally, t...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 1 P1.6* The reference direction for iab points from a to b. Because iab has a negative value, the current is equivalent to positive charge moving opposite to the reference direction. Finally since electrons have negative charge, they are m...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 5 P3.31* L = 2H v L (t ) = L diL (t ) dt p (t ) = v L (t )iL (t ) w (t ) = 1 L[iL (t )] 2 2 P3.36* iL (t ) = L 0 1 t v L (t )dt + iL (0 ) 3 = 20 10 5 t 10dt 0.1 0 = 2 10 t 0.1 A Solving for the time that the current r...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 5 P3.40* L = 2H v L (t ) = L diL (t ) dt p (t ) = v L (t )iL (t ) w (t ) = 1 L[iL (t )] 2 2 P3.45* iL (t ) = L 0 1 t v L (t )dt + iL (0 ) 3 = 20 10 5 t 10dt 0.1 0 = 2 10 t 0.1 A Solving for the time that the current r...
UC Riverside >> EE >> 002 (Spring, 2008)
Homework # 6 P5.53* This is a capacitive load because the reactance is negative. 2 P = I rms R = (15) 2 100 = 22.5 kW 2 Q = I rms X = (15) 2 ( 50) = 11.25 kVAR Q = tan 1 = tan 1 ( 0.5) = 26.57 P power factor = cos( ) = 89.44% P5.59* I= 1000 20 ...
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