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COMMENTS ON CHAPTER 9 March 17, 2008 This chapter is all about the set U(R) of units of a &lt;a href=&quot;/keyword/commutative-ring/&quot; &gt;commutative ring&lt;/a&gt; R. The main focus is on the set U(Z/mZ). This set consists of the units (also called invertible elements ) of Z/mZ. Any general statement about U(R) applies, in particular, to U(Z/mZ), since Z/mZ is a &lt;a...

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THE PRIMITIVE ELEMENT THEOREM April 15, 2008Primitive Element Theorem. Let F be a nite eld, and let U be its set of units, the non-zero elements of F . Let n = |U |, the number of elements in U (so that n = |F |1). Then U has an element whose order
310 Introduction to Modern Algebra Instructor: Petronela Radu April 4, 2008Sample Problems for Exam 21. Find all units in Z/12Z. For each unit find its order and its inverse. 2. In a commutative ring R denote by U (a) = {a u|u R, u is a unit},
221 - Differential Equations Instructor: Petronela Radu November 1, 2005Project 2 - Due December 1You may work on this project individually, in groups of two, three, or four. If this is a group project, write how each of the group members contribu
398 Math in the City Instructor: Petronela Radu September 8, 2006Homework 1Due September 181. (30 points) What condition must be unknowns x, y, and z has a solution? x 2x x placed on a, b, and c so that the following system in + 2y 3z = a + 6
MATH 324/824, Fall 2008 Introduction to Partial Differential Equations (PDEs)MWF 11:30 AM - 12:20 PM, Burnett Hall 102Instructor Petronela Radu Avery Hall 239 (402) 472-9130, Grading Homework and Projects Midterms Final Exam 20% 25% x 2 30% pradu@m
324 Introduction to PDEs Instructor: Petronela Radu September 11, 2006Homework 2Due September 20Before writing your solutions commit yourself to being correct and clear throughout your arguments. In order to receieve any credit the grader must be
324 Introduction to PDEs Instructor: Petronela Radu August 30, 2006Homework 1Due September 8Before writing your solutions commit yourself to being correct and clear throughout your arguments. In order to receieve any credit the grader must be abl
324 Introduction to PDEs Instructor: Petronela Radu September 12, 2008Homework 2Due September 24Before writing your solutions commit yourself to being correct and clear throughout your arguments. In order to receieve any credit the grader must be
324 Introduction to PDEs Instructor: Petronela Radu October 3, 2006Homework 4Due October 11Before writing your solutions commit yourself to being correct and clear throughout your arguments. In order to receive any credit the grader must be able
324 Introduction to PDEs Instructor: Petronela Radu October 10, 2008Homework 4Due October 22Before writing your solutions commit yourself to being correct and clear throughout your arguments. In order to receieve any credit the grader must be abl
324 Introduction to PDEs Instructor: Petronela Radu October 20, 2006Homework 6Due October 27Before writing your solutions commit yourself to being correct and clear throughout your arguments. In order to receive any credit the grader must be able
324 Introduction to PDEs Instructor: Petronela Radu November 9, 2006Homework 9Due November 17Before writing your solutions commit yourself to being correct and clear throughout your arguments. In order to receive any credit the grader must be abl
Math 398 Fall 2008 Petronela RaduHomework 1 First draft due September 15 Final draft due September 29The list below contains some of the green features that belong to sustainable design. You are to research and write about one of these features
UNL - JLOGAN - 1
Mathematics 842 (Applied Mathematics I)Fall Semester 2008Instructor: J. David Logan Time: 12:30 MWF Text: J. David Logan, 2006. Applied Mathematics 3rd ed., Wiley Interscience. (Ch 6, 7, 8 and parts of Ch 4 and Ch 5) Prerequisites: Elementary line
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REQUEST FOR TRAVEL FUNDS Department of Mathematics &amp; Statistics Date:_Name: Destination: Will you give a talk? Additional Purpose for Travel: Meeting (please specify name of meeting): _ Invited _ Contributed _ Length__Departing Lincoln:_ Arrivin
UNL - RDIETER - 1
Getting StartedFirst of all, we need your machine to be booted into Linux. If it isn't already displaying RedHat Linux on the screen, then either turn the machine on, or, if it is already on, issue a shutdown/restart sequence.LILOWhen the machine
UNL - RDIETER - 1
TeX1. TeX is command-line driven. Gone are most of the nice menu-driveness we've seen with NEXTSTEP. To tex/latex a file, open a terminal window and use the tex or latex commands: &gt; latex latextest.tex 2. DVI: The dvi viewer available is called kdvi
UNL - BHARBOURNE - 1
Revised 11-2003 REIMBURSEMENT OF EXPENSES AND RECEIPT OF AN HONORARIUM FOR AN ACADEMIC VISITB-1 and WB visa classifications: The visitor may be reimbursed for travel associated with the visit. He or she also may be reimbursed for lodging and/ or me
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Getting StartedFirst of all, we need your machine to be booted into Linux. If it isn't already displaying RedHat Linux on the screen, then either turn the machine on, or, if it is already on, issue a shutdown/restart sequence.LILOWhen the machine
UNL - ICAPGS - 98
-INTERNATIONAL CONFERENCE ON ALGORITHMIC PROBLEMS IN GROUPS AND SEMIGROUPS CONFERENCE SCHEDULE_ SUNDAY, May 104:00-8:00pm Registration (at dormitory, hotels)_
UNL - MBRITTENHA - 2
From mmk8@cornell.edu Mon Mar 11 14:13:08 1996Posted-Date: Mon, 11 Mar 1996 15:12:27 -0600X-Sender: mmk8@postoffice2.mail.cornell.eduMime-Version: 1.0Content-Type: text/plain; charset=&quot;us-ascii&quot;Date: Mon, 11 Mar 1996 16:11:31 +0400To: mmk8@corn
UNL - MBRITTENHA - 2
There you will nd copies of nearly every handout from class, lists of homework problems assigned, dates for exams, etc. O ce Hours: tentatively Mo 11:00-12:00, Tu 2:00 - 3:00, We 1:00-2:00, and Th 1:00 2:00, and whenever you can nd me in my o ce and
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
Curriculum Vitae Mark Brittenham Department of Mathematics and Statistics 203 Avery Hall University of Nebraska - Lincoln Lincoln, NE 68588-0323 Phone: (402)-472-7222 E-mail address: mbritten@math.unl.edu WWW: http:/www.math.unl.edu/mbritten/ Educati
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
Idea: If two or more quantities are related a change in one value means a change in others, then their rates of change are related, too. xyz = 3 ; pretend each is a function of t, and di erentiate implicitly. General procedure: Draw a picture, descri
UNL - MBRITTENHA - 2
The basic question: what is the best way to choose the best of several alternatives, based on the preferences of some group of people? For example, how do a group of people choose which restaurant to eat dinner at, based on the culinary preferences o
UNL - MBRITTENHA - 2
Technically, everything covered on the rst exam, plus.Math 1650 Topics for second examChapter 2: Polynomials x3: Polynomial division root a of f \$ factor x , a of f x reason: polynomial long division f x = x , agx + b ; a=root, then b=0x4:x5:
UNL - MBRITTENHA - 2
Math 445 Number Theory Introduction to/Review of concepts from abstract algebra An integer p is prime if whenever p = ab with a, b Z, either a = n or b = n . [For sanity's sake, we will take the position that primes should also be 2 .] Fundamental
UNL - MBRITTENHA - 2
Math 107H Calculus II Section 003 Lecture: MTWRF 9:30-10:20 Military and Naval (M&amp; N) B6 Instructor: Mark Brittenham Oce: Avery Hall (AVH) 317 Telephone: (47)2-7222 E-mail: mbrittenham2@math.unl.edu WWW: http:/www.math.unl.edu/mbrittenham2/ WWW pages
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
Math 107H Calculus II Section 004 Lecture: MTWRF 9:30-10:20 Military and Naval (M&amp; N) B6 Instructor: Mark Brittenham Oce: Oldfather Hall (OldH) 819 Telephone: (47)2-7222 E-mail: mbritten@math.unl.edu WWW: http:/www.math.unl.edu/mbritten/ WWW pages fo
UNL - MBRITTENHA - 2
Math 208McFee's Math Circus1st Semester, 99-00Introduction: You have been hired by McFee's Mathematical Circus to find the optimal design for their &quot;big top&quot; tent, utilizing 1000 square meters of canvas. There are two competing designs, and the
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
Math 445 Number Theory October 4, 2004 Proposition: If f is a polynomial with integer coefficients and (M, N ) = 1, then the congruence equation f (x) 0 (mod M N ) has a solution the equations f (x) 0 (mod M ) and f (x) 0 (mod N ) both do. The di
UNL - MBRITTENHA - 2
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Math 445 Number Theory November 1, 2004 From last time: x = [a0 , a1 , . . . , an , . . . ] ; set rn = [a0 , . . . , an ] = hn x as n . kn hn 1 1 . Then |x - rn | &lt; 2 . In particular, kn kn kn+1 kn an+1a From this, we can learn many things! Fir
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
Math 445 Number Theory November 19, 2004 Theorem: If abc is square-free, then ax2 + by 2 + cz 2 = 0 has a (non-trfvial!) solution x, y, z Z a, b, c do not all have the same sign, and each of the equations have solutions. w2 -ab (mod c), w2 -ac (m
UNL - MBRITTENHA - 2
UNL - MBRITTENHA - 2
Math 445 Number Theory October 00, 2004 We have seen (because there is a primitive root mod pk for p an odd prime): Theorem: If p is an odd prime, k 1, and (a, p) = 1, then the equation x a (mod p ) has a solution an k(pk ) (n,(pk ) 1 (mod pk
UNL - MBRITTENHA - 2
Math 445 Homework 8 Solutions 36. Let hn /kn (as usual) denote the nth convergent of the continued fraction expansion of the hn a irrational number x. Show by example that it is possible for b &lt; kn+1 and x- &lt; x- b kn . Most any irrational number wor
UNL - MBRITTENHA - 2
This fall we will be offering a new course, Math 873Differential and Geometric Topology. While waiting forthe graduate catalog to catch up with the department,we will offer the course this fall as Math 856(Differental Geometry).The prerequisi
UNL - MBRITTENHA - 2
Errata for TOPOLOGY,second edition.xii, 13 of connectedness and compactness in Chapter 3.107; 2 f maps [0,1) into S super 1111; 15 The wording is confusing. Try this: Let X and X' be spaces having the same underlying set; let th
UNL - MBRITTENHA - 2
restart: with(numtheory); printlevel:=0: prmstart:=29: expstart:=200: expend:=300: p:=nextprime(prmstart): test:=false: for k from expstart to expend while evalb(test=false) do n:=p*(2^k)+1; test:=isprime(n): end do; cat(`k = `,k); cat(`n = `,n);
UNL - MBRITTENHA - 2
Math 445 Homework 2 Due Wednesday, Sept. 175. Show, by induction, that for every n N, f (n) = (Note, however, that it is not a multiple of n !)1 4 1 3 1 n + n + n is an integer. 2 3 61 1 1 + + = 1, which is an integer. This 2 3 6 gives us our
UNL - MBRITTENHA - 2
Math 445 Number Theory August 23 and 25, 2004 Number theory is about finding and explaining patterns in numbers. Ulam Sprial:36 35 34 33 32 31 30 37 16 15 14 13 12 29 38 17 4 3 2 11 28 39 18 5 0 1 10 27 40 19 6 7 8 9 26 41 20 21 22 23 24 25 42 43 4
UNL - MBRITTENHA - 2
hep-th/0503159arXiv:physics/0503159v2 [physics.gen-ph] 14 Apr 2005Fast Factoring of IntegersGordon Chalmers e-mail: gordon@quartz.shango.comAbstract An algorithm is given to factor an integer with N digits in lnm N steps, with m approximately
UNL - MBRITTENHA - 2
The Lucas-Lehmer test can decide whether or not a Mersenne number M=2^N-1 is prime. It requiresthat you compute A_{N-1}, where A_1=4 and A_{i+1}=(A_i)^2-2. Below, since the first &quot;T&quot; computedis A_2, we stop the loop at N-2. If the number &quot;S&quot;, that
UNL - MBRITTENHA - 2
with(numtheory); printlevel:=0;a:=1; for i from 1 to 20 do a:=2*a: print(i,a); end do;N:=1234567; while N&gt;0 do B:=floor(log(N)/log(2); print(B); N:=N-2^B: end do;
UNL - MBRITTENHA - 2
This worksheet will build an RSA public key system for you.Enter your favorite (large) numbers inside the parenthesesfor &quot;p&quot; and &quot;q&quot;; the worksheet will find the smallest primeslarger than your numbers, and take their product to buildyour modulus
UNL - MBRITTENHA - 2
with(numtheory); a := 142111; n := 56333333333333333333; b := a&amp;^(n-1) mod n;ithprime(100000);
UNL - MBRITTENHA - 2
We start by setting up some variables. &quot;N&quot; is the number we are testing for primality. Some choices which foil some of the tests are 2047 , 25326001 . 561 is fun, too. &quot;a&quot; is the base we will test on. Change &quot;printlevel&quot; to 1 to stop supressing th
UNL - MBRITTENHA - 2
From - Thu Oct 09 08:13:01 1997Path: news.unt.edu!cs.utexas.edu!howland.erols.net!vixen.cso.uiuc.edu!orion.math.uiuc.edu!danFrom: baez@math.ucr.edu (john baez)Newsgroups: sci.math.researchSubject: Low-dimensional topology and quantum gravityDate
UNL - MBRITTENHA - 2
Workshop on Geometric Group Theory and Computer Science = VenueJuly 5-9, 1998. Mount Holyoke College, South Hadley, MA.This workshop is one of the 1998 AMS-IMS-SIAM Joint Summer Research Conferences in the Mathematical Scien
UNL - MBRITTENHA - 2
Announcing the Summer 1997 Wasatch Topology Conference The mathematics departments of Brigham Young University and the University of Utah along with the National Science Foundation are sponsoring the sixth semiannual Wasatch Topology Conference
UNL - MBRITTENHA - 2
From - Sun Jun 30 14:50:40 1996Path: bubba.NMSU.Edu!lynx.unm.edu!tesuque.cs.sandia.gov!ferrari.mst6.lanl.gov!newshost.lanl.gov!ncar!csn!nntp-xfer-1.csn.net!magnus.acs.ohio-state.edu!math.ohio-state.edu!uwm.edu!vixen.cso.uiuc.edu!symcom.math.uiuc.edu
UNL - MBRITTENHA - 2
From mgc@uoknor.edu Thu Mar 28 22:04:54 1996Posted-Date: Thu, 28 Mar 1996 23:03:57 -0600X-Sender: mgc@math.uoknor.edu (Unverified)X-Mailer: Windows Eudora Version 1.4.4Mime-Version: 1.0Content-Type: multipart/mixed; boundary=&quot;=_828079230=_&quot;To:
UNL - MBRITTENHA - 2
From brick@mathstat.usouthal.edu Mon Nov 24 21:03:02 1997Mime-Version: 1.0Content-Type: text/plain; charset=&quot;us-ascii&quot;Date: Mon, 24 Nov 1997 21:33:38 -0400To: From: Stephen Brick &lt;brick@mathstat.usouthal.edu&gt;Subject: G^3Content-Length: 1146