Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.
1 Page
Document Preview
225A MATH PROBLEM SHEET II JANUARY 26, 2006 1. Find the ring of integers, and calculate the discriminant of Q( 3 5). 2. Find the ring of integers, and calculate the discriminant of Q( 2, i). 3. Marcus, Chapter II, Exercise 22. 4. Marcus, Chapter II, Exercise 28. 5. Let be a root of the polynomial T 3 2T + 2. Calculate the ring of integers of Q(). 6. Let K be a number eld with [K : Q] = n, and let 2t of the n...
Unformatted Document Excerpt
Coursehero >> California >> UCSB >> MATH 225aCourse Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
225A MATH PROBLEM SHEET II JANUARY 26, 2006 1. Find the ring of integers, and calculate the discriminant of Q( 3 5)....
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Below is a small sample set of documents:
Below is a small sample set of documents:
UCSB - MATH - 225a
MATH 225A PROBLEM SHEET I JANUARY 19, 2006 1. Which the of following numbers are algebraic integers: (i) 12 15( 39 7 + 7 39) (ii) 1+i 2 2.(i) Let d be a squarefree integer. Find the ring of integers of Q( d). (ii) Let d be a squarefree integer w
UCSB - MATH - 225a
MATH 225A PROBLEM SHEET III FEBRUARY 6, 2006 1. Let p be an odd prime, and let p be a primitive pth root of unity. Set = Gal(Q(p )/Q), and let : C be a character of order n > 1 (i.e. is a group homomorphism, and n is the least integer such that
UCSB - MATH - 227b
Syllabus for Math 227B: Automorphism GroupsWinter 2006 Instructor: Jon McCammond Oce hours: M 12:00-1:50, W 12:00-12:50 or by appointment in South Hall 6711 Phone number: 893-2060 (no answering machine) E-mail: jon.mccammond@math.ucsb.edu My Home Pa
UCSB - MATH - 227c
Syllabus for Math 227C: Geometric Group TheorySpring 2005 Instructor: Jon McCammond Oce hours: T 1:00-1:50, Th 12:00-1:50 or by appointment in South Hall 6711 Phone number: 893-2060 (no answering machine) E-mail: jon.mccammond@math.ucsb.edu My Home
UCSB - MATH - 241a
Math 241AInstructor: Guofang Wei Fall 2000The basic idea of this course is that curvature bounds give information about manifolds, which in turn gives topological results. A typical example is the Bonnet-Myers Theorem. Intuitively, Bigger curvature
UCSB - MATH - 241a
Dr. LeRoy: 2024 North Hall Office hours by appointment Email sleroy@econ.ucsb.eduEconomics 241A Econometrics Fall 2007Lectures Tuesday-Thursday 12:30 1:45, North Hall 2111 Section W 10-10:50, North Hall 2111 Instructor: Stephen F. LeRoy. Office:
UCSB - MATH - 241b
Math 241BInstructor: Guofang Wei Winter 2000-2001Last quarter we studied the relationship between Ricci curvature and topology. The basic tools were: 1. Volume Comparison 2. Laplacian Comparison 3. Excess Estimate This quarter we study the relation
UCSB - MATH - 260ee
MATH 260DD SYLLABUS WINTER 2005 Lectures TR 11:00-12:15, Girvetz 2124. Instructor James Mc Kernan, South Hall 6713, phone 893-3579 Oce Hours or by appointment, if you cannot make these times. Text Principles of Algebraic Geometry Philip Grith and Jos
UCSB - MATH - 260ee
3. Smoothness, Singularities and Quotients Proposition 3.1. Let F be a fan. Then X(F ) is smooth i F , is generated by a collection of vectors, which can be augmented to a basis of N . Proof. Clearly we may assume that X = U . If does not span NR
UCSB - MATH - 260ee
1. Algebraic Groups Denition 1.1. An algebraic group G is a group, which is a variety where both the multiplication map : X X X and the inverse map i : X X are algebraic. Example 1.2. The group of n m matrices is an algebraic group under additio
UCSB - MATH - 260ee
2. Toric Varieties Via Algebraic Groups: Denition 2.1. Let X be a normal variety, and let D be a divisor on X. We say that the pair (X, D) is a toric variety if U = X D is isomorphic to a torus, and the natural action of U on itself, extends to an a
UCSB - MATH - 3h
MATH 3H SYLLABUS SPRING 2003 Lectures W 12:00-1:15pm, Modular Bldg 103Instructor James Mc Kernan, South Hall 6713, phone 893-3579 Oce Hours Monday 1:00-3:30, Wednesday 10:00-11:00, 2:30-3:30, or by appointment, if you cannot make these times. Text
UCSB - MATH - 3h
MATH 3H SYLLABUS WINTER 2003 Lectures Instructor Oce Hours W 12:00-1:15 James Mc Kernan, South Hall 6713, phone 893-3579 Monday 1:00-3:30, Wednesday 10:00-11:00, 2:30-3:30,or by appointment, if you cannot make these times. Grading policy Anyone who
UCSB - MATH - 3h
MATH 3H SYLLABUS AUTUMN 2002 Lectures Instructor Oce Hours W 1:00-2:15 James Mc Kernan, South Hall 6713, phone 893-3579 Monday 1:00-3:30, Wednesday 10:00-11:00, 2:30-3:30,or by appointment, if you cannot make these times. Grading policy Anyone who
UCSB - MATH - 3h
MODEL ANSWERS TO THE FIRST HOMEWORK 1. LIKE MANY OF THE GREAT GENERALS OF HISTORY CAESAR SEEMS TO HAVE BEEN SADLY LACKING IN CRYPTOGRAPHIC SUBTLETY. The cylinder circumference is seven units long. 3. (a) Arrange the letters of the message in a zig-za
UCSB - MATH - 5ai
Math 5AI - Jacob Course Information and Syllabus Winter Quarter 2006Instructor: Bill Jacob Oce Hours: Wednesdays 9:30 - 12:30, held in South Hall 6719. Also by appointment. Phone: x8048 email: jacob@math.ucsb.edu Teaching Assistant; Brie Finegold em
UCSB - MATH - 5bi
UCSB - ECE - 1
Lecture 8 - Chirp and Dispersion CompensationECE 228A Fall 2008 Daniel J. Blumenthal8.1 Laser Chirp Another important parameter is the laser frequency chirp (frequency shift) Chirp will limit the bit-rate-distance product that a link can supp
UCSB - ECE - 1
ECE 162A Mat 162A Lecture #6: Stationary Solutions y Read Chapter 5,6 of Eisberg,ResnickJohn Bowers Bowers@ece.ucsb.eduEigenvalue Equation Using operators, Schroedingers equation can gp , g q be expressed as an eigenvalue equationh2 d 2 Eop =
UCSB - ECE - 105
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 4, APRIL 1999471Continuum Modeling of the Dynamics of Externally Injection-Locked Coupled Oscillator ArraysRonald J. Pogorzelski, Fellow, IEEE, Paolo F. Maccarini, and Robert A.
UCSB - ECE - 125
UCSB - ECE - 130a
hg `vmk r t hg `vmk r t wu wu k q 1o n | ~w ~} w l ow n w ow n w w lhh h f i hf h mku i p } mk q w k{ o r l Gz ku i p } k q w k{ r ml Gzhg `vmk r t wu w ~} 1~o n | w l ow n w hg `vmk r t wu mk q w l ow n ow f
UCSB - ECE - 130a
ty b ` U FvstU y e SU e B QE S G sU BG s BE Q SE sGB s SE G sU G V U U B ` E s s sE ` DaITgs!RWF@WT!fPsuWHkFW~h~P|FHTWWUWuFas2PBF!BTDvB y yBGB r SB eu BGE sU S eIE G V e B I e e'w6cDW'}D}w8mDRmDDwmpDkWfhkhTaTfH%WTT
UCSB - ECE - 130a
ot n l q FD l G3eIBG t qD @ l t q F $dGC`eIBGD g WP e P v D WB F P @ e FWS P 7yb#37R`VP`y!RUIBf!Rc n ` n BS @ ECVBD D ACfW n F gcf BP Fe F B FW T@D P xW @ | H B g`RY CVDyCI@f7IC#7EA1rCS fRIP3C@ xWeB T v D P FD x F v T e B F Q W T
UCSB - ECE - 132
UCSB - ECE - 132
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 48, NO. 12, DECEMBER 20002573A 310-GHz GaN-Based Flip-Chip Integrated Broad-Band Power AmplifierJane J. Xu, Stacia Keller, Gia Parish, Sten Heikman, Umesh K. Mishra, Fellow, IEEE, and Ro
UCSB - ECE - 134
ECE 134Introductory ElectromagneticsProf. YorkReview of Transmission-Line TheoryThe term transmission-line in electromagnetics is commonly reserved for those structures which are capable of guiding TEM waves. Transmission-lines are a special c
UCSB - ECE - 137b
AMPLIFIER AND COMPARATOR CIRCUITS AUDIO CIRCUITSAPP 1760: Sep 28, 2002Class D Audio Amplifiers Save Battery LifeThis application note examines the operation and benefits of a Class D (switch-mode) audio amplifier. Switch-mode amplifiers such as
UCSB - ECE - 139
UCSB - ECE - 140
A Compact Coaxial Waveguide Combiner Design For Ultra-Broadband Power AmplifiersPengcheng Jia, Robert A. York E.C.E. Dept., University of California, Santa Barbara, CA 93106, USAAbstract We report an enhanced broadband passive combiner structure
UCSB - ECE - 144
UCSB - ECE - 144
$ 1/7/%DVHG ,QWHJUDWHG &LUFXLW IRU D *+] 91$ 6\VWHP2 :RKOJHPXWK % $JDUZDO 5 3XOOHOD ' 0HQVD 4 /HH - *XWKULH 0 - : 5RGZHOO 5 5HXWHU - %UDXQVWHLQ 0 6FKOHFKWZHJ . .|KOHU )UDXQKRIHU ,QVWLWXW ,$) 7XOODVWU ' )UHLEXUJ *HUPDQ\ 3KRQH )D[ (PDLO ROZR#LDI
UCSB - ECE - 147a
Lab 1: PID Control193Lab 1: PID Control3.1 OutlineIn this experiment you will identify and design controllers for a \black box" with an unknown second order transfer function. The physical system is very close to linear as it is a simple op-
UCSB - ECE - 147a
UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Electrical and Computer EngineeringLaboratory Experiments ECE 147a (Fall 95)Copyright c 1995, Roy Smith This material is provided solely for the use of students enrolled in ECE 147a at the Uni
UCSB - ECE - 147a
UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Electrical and Computer EngineeringMatlab Computer Modules ECE 147a (Fall 95)Copyright c 1995, Roy Smith This material is provided solely for the use of students enrolled in ECE 147a at the Un
UCSB - ECE - 147b
ECE 147b: (Winter 2009) Introduction1ECE 147b Digital Control Systems; Theory and Design Winter 2009Description The course will include the following topics. Analog/Digital & Digital/Analog conversion, Sampled data Systems Digital Design via t
UCSB - ECE - 147b
Direct digital design Calculating C(z) to control P (z)Continuous-time designP(s)C(s)Model P(s), and sample/hold as P(z)Approximation of C(s) with C(z)P(z)Discrete-time designC(z) ZOH equivalence gives P (z). Design C(z) for good clo
UCSB - ECE - 148
UCSB - ECE - 151
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 3, MARCH 2002937Active Integrated AntennasKai Chang, Fellow, IEEE, Robert A. York, Senior Member, IEEE, Peter S. Hall, Fellow, IEEE, and Tatsuo Itoh, Fellow, IEEEInvited Paper
UCSB - ECE - 151
8OWUD KLJK IUHTXHQF\ +%7 LQWHJUDWHG FLUFXLWV4 /HH ' 0HQVD - *XWKULH 0 5RGZHOO 6 /RQJ 6& 0DUWLQ 536PLWK < %HWVHU 6 -DJDQDWKDQ 7 0DWKHZ 3 .ULVKQDQ & 6HUKDQWULF VXEVWUDWH 'HPRQVWUDWHG VPDOOVFDOH ,&V LQ WKH SURFHVV WR *+] *+] VWDWLF IUHTXHQF\ GLYL
UCSB - ECE - 154
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 5, MAY 20021355Multioctave Spatial Power Combining in Oversized Coaxial WaveguidePengcheng Jia, Student Member, IEEE, Lee-Yin Chen, Student Member, IEEE, Angelos Alexanian, Membe
UCSB - ECE - 158
IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 12, NO. 7, JULY 2002237A New High Performance Phase Shifter using BaxSr1 xTiO3 Thin FilmsBaki Acikel, Troy R. Taylor, Peter J. Hansen, James S. Speck, and Robert A. YorkAbstractIn this paper,
UCSB - ECE - 160
952IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 3, MARCH 2003Synchronization Design of a Coupled Phase-Locked LoopJames F. Buckwalter, Student Member, IEEE, Ted H. Heath, and Robert A. York, Senior Member, IEEEAbstractCoup
UCSB - ECE - 178
AC Loss Modeling in Ba0.5Sr0.5TiO3 Using Dielectric Relaxation Nadia K. Pervez1, Jiwei Lu2, Susanne Stemmer2, Robert A. York1 1 Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, U.S.A. 2 Materials D
UCSB - ECE - 178
UCSB - ECE - 183
HIGH FREQUENCY LOSS MODELING USING UNIVERSAL RELAXATIONNadia K. Pervez, Jaehoon Park, Jiwei Lu, Susanne Stemmer, and Robert A. York Electrical and Computer Engineering and Materials Departments University of California, Santa Barbara CA 93106 Unive
UCSB - ECE - 183
UCSB - ECE - 189a
CS189A/172 - Winter 2008Lecture 1: IntroductionCMPSC 189A/172 Lectures: Monday/Wednesday/Friday 1:00-1:50PM, 387 101 Discussions: Friday 3:00-3:50 PHELP Instructor: Tevfik Bultan bultan@cs.ucsb.edu, Phone: x3735 Office Hours: Monday, Friday 2:
UCSB - ECE - 193
Rutile lms grown by molecular beam epitaxy on GaN and AlGaN / GaNP. J. HansenMaterials Department, University of California, Santa Barbara, California 93106V. VaithyanathanDepartment of Materials Science and Engineering, The Pennsylvania State U
UCSB - ECE - 196
A 24 GHz Wafer Scale Electronically Scanned Antenna Using BST Phase Shifters for Collision Avoidance SystemsShawn Shi*, Joe Purden Delphi Electronics and Safety 3011 Malibu Canyon Road, Malibu, CA 90265 Jean Jin, Robert A.York Agile Materials and Te
UCSB - ECE - 196
UCSB - ECE - 199
IEEE MTT-S 2001 International Microwave Symposium Digest, Vol. 3 pp. 1713-1716185 GHz Monolithic Amplifier in InGaAs/InAlAs Transferred-Substrate HBT TechnologyM. Urteaga, D. Scott, T. Mathew, S. Krishnan, Y. Wei, M.J.W. Rodwell Department of Elec
UCSB - ECE - 210a
UCSB - ECE - 210a
UCSB - ECE - 210a
UCSB - ECE - 210a
UCSB - ECE - 217
UCSB - ECE - 225
Chapter6MODELS OF PROCESS VARIATIONS IN DEVICE AND INTERCONNECTDuane Boning Massachusetts Institute of Technology Sani Nassif IBM Austin Research Laboratory6.1 INTRODUCTION: SOURCES OF VARIATIONVariation is the deviation from intended or desi
UCSB - ECE - 225
Cramming More Components onto Integrated CircuitsGORDON E. MOORE, LIFE FELLOW, IEEEWith unit cost falling as the number of components per circuit rises, by 1975 economics may dictate squeezing as many as 65 000 components on a single silicon chip.
UCSB - ECE - 226
Molecular Beam Deposition of Low-Resistance Polycrystalline InAsD. Scott, M. Urteaga, N. Parthasarathy, J.H. English and M.J.W. Rodwell Department of Electrical and Computer Engineering University of California, Santa Barbara, CA 93106 Tel: (805) 89
UCSB - ECE - 227a
ECE 227A Syllabus Fall 08Instructor: Lecture times: Office hours: Primary text: Secondary text: Prof. Larry A. Coldren MW 12-2 MW 2 (W may have conflicts) Diode Lasers and Photonic Integrated Circuits Coldren & Corzine; Wiley; ISBN: 0-471-11875-3 O