HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS?

Size: px
Start display at page:

Download "HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS?"

Transcription

1 6th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS? Cecília Sitkuné Göömbei College of Nyíegyháza Hungay Abstact: The Intoduction of Infomatics subject deals with the udiments of infomatics within the education system of the College of Nyíegyháza whee infomatics teaches and pogamme mathematics ae tained as well. The poblem that made us examining the subject is that thee has been high ate of failed exams in this subject since yeas. In the fist semeste of 2004/2005 the 83% of the examinees failed at the fist exam and afte the 2 nd, 3 d o 4 th exam still the 47% of the students wee unsuccessful. The aim of this pape is to a) intoduce the content, the equiements and the concete exam equiements of the Intoduction of Infomatics subject, b) the mathematical backgound of the execises and c) the solutions of one basic execise of the test. Based on 646 test papes we ty to detemine the most common mistakes and based on the expeience we make suggestions. Keywods: infomatics, education, numeical systems.. INTRODUCTION Within the taining system of the College of Nyíegyháza fo infomatics teaches and pogamme mathematics the Intoduction of Infomatics subject that is about udiments of infomatics is an obligatoy subject in the fist semeste. Thee is lectue in evey week, the numbe of the cedit points is 2 and at the end of the semeste the examinees have to take teminal examination. The poblem that that made me examining the subject is that thee has been high ate of failed exams in this subject since yeas. The exam esults of the fist semeste of the yea 2004/2005, as it follows: At the fist exam thee wee 349 students with the following esults: excellent: 2 people good: 0 people satisfactoy: 3 people pass: 3 people unsatisfactoy: 293 people; aveage:,27 The following diagam shows the maks of the fist exam in pecentage:

2 The maks of the fist exam 83% %3% 4% 9% excellent good satisfactoy pass unsatisfactoy Figue. The esults of the fist exam At the end of the examination season (afte epeated exam) not moe than 47% of the students concened passed the examination. The total esults can be seen below: Total 53% 3% 0% % 23% excellent good satisfactoy pass unsatisfactoy Figue 2. Total esults 2. THE CONTENT OF THE SUBJECT, THE METHOD OF EXAMINING 2.. The main aim of the subject is to make the students familia with the theoetical base and technical tems of infomatics. To ecapitulate: I. The compute and the algoithm: The notion of the compute, the Neumann-pinciples, inne build-up of the compute, the peipheal devices; The notion of algoithm, descipto devices, complexity. II. Infomation and data epesentation: Measuing the infomation, entopy, decimal value numbe epesentation, numeical systems, fixed point epesentation, floating point epesentation, decimal epesentations, logic data, chaacte, sting epesentation, logic opeations and thei tuth tables, logic opeations of fixed point numbes. III. Data stuctues and thei epesentations: Linea data stuctues: aays, linked lists, odeing, special linea data stuctues: stack, evaluation of postfix expession, tansfom infix expession to postfix, pogession.

3 Non-linea data stuctue: ecod data stuctue, gaph data stuctue 2.2. The teminal examination is in witten fom. The test (0 execises) has to be solved within 30 minutes and calculato cannot be used. The examinees get the test in pinting, they can count on the test, the esults should be copied in a box beside the execises. Duing the coection these esults ae taken into consideation. The maximum points fo the execises ae 0, 0,5 o point. The maks depend on the points and ae counted the following way: 9,5-0 excellent (5) 8,5-9 good (4) 7,5-8 satisfactoy (3) 6,5-7 pass (2) To be able to solve the execises of the test the following knowledge is equied:. Convet fom decimal system 6. Logic opeations 2. Convet to decimal system 7. Convet fom floating point fom 3. Convesion infix expession to 8. Convet to floating point fom postfix 9. Convet between numeical systems 4. Convesion to binay complement 0. Convesion fom binay complement 5. Counting infomation content It can be seen fom the test that the most stessful expect two execises it occus in evey execise topic is the numeical system topic. If we take into consideation the efficient solutions we can daw the conclusion that expect the execise 0. less then 50% of the students can solve the execises (the aveage is unde 40%!). The following diagam shows the efficiency by execises: Efficiency by execises efficiency 00% 80% 60% 40% 20% 0% o 0,5 point point numbe of the execise Figue 3. Efficiency by execises 3. MATHEMATICAL BACKGROUND OF THE EXERCISES [] 3.. The notion of the decimal value numeical system The based decimal value numeical system is defined by the following theoem: i 2 2 (... a 2 a a 0. a a 2 ) = ai = + a + a + a + a + a + () i= 2 0 2

4 The numbe is the base figue of the numeical system, the signs a i ae the numeals of the numbe, the ai numbe maked by the a i is called the fomal value of the numbe, the i powe is the decimal value of the numbe ( i = 0, ±, ± 2,...), and. is the point of efeence Switch fom one numeical system to anothe one 3.3. theoem Let 2 be a natual numbe. In this case an abitay v 0 eal numbe can be noted in the based decimal value numeical system v = ( a n a n... a 2 aa 0. a a 2...) (2) fom, whee 0 a i natual numbe fo all i = n, n-, and a 0, if n. v intege pat: n factional pat: [] v ( a n a n... a 2 aa 0.0) =, (3) Let based numeical system. {} v ( 0. a a 2...) =. (4) v 0 is a given numbe in the R based numeical system. Define the numeals of v in the Fist define the numeals of v intege pat: based on the theoem.3. [ v ] can be witten fom, in anothe way a n n n + an + + a + a0 (5) (...(( an + an ) + an 2 ) + + a) + a0 (6) Pefom the esiduum division with ; the esiduum based on thei inceasing decimal value give the fomal values of the numeals in the based numeical system: [] v = v + a0 v = v2 + a v2 = v3 + a2 (7) vn = vn + an vn = 0 + an Now define the numeals of the factional pat of v : based on the theoem.3. { can be witten in fom. Thus 2 a + a + (8) 2 {} v = a + a 2 +, (9) whee the intege pat of {} is, the factional pat is a +. Multiply by the v a 2 factional pat of the poducts of multiplication. These poducts ae always fom the peceding v}

5 steps. The intege pat of the poducts give by deceasing intege pat the fomal values of the numeals in the {} v based numeical system. Since we did the opeations in the oigin (R based) numeical system the fomal values of numeals as the esults of the steps taken ae also in this numeical system. Afte this we wite the numeals which mak the fomal values of the numeals in the based numeical system, in the places of the fomal values: so we get the fom of v in the based numeical system. 4. THE COMMON MISTAKES IN THE EXERCISE. The concete execise: Convet the given numbe fom decimal system to numeical system of based thiteen in a way that the factional should be 3-digit coect! The numbe is: ~The students note the execise wongly, they do not count with the numbes in the execise. ~Counting mistakes - The most of the counting mistakes occu in the dividing. The students detemine wongly the numeals in the quotient o the esiduum, but mostly both. They cannot do division with 2-digit diviso confidently. - In the multiplications the typical counting mistakes that pimay school students also often make ae fequent, fo example: 9 x 9 = 8; 6 x 3 = 2. They have poblem in multiplying with 2-digit numbe, they multiply the multiplicand with only one decimal value. Vey fequently they define wongly the place of the point of efeence (decimal point). ~ Defectiveness in the udiments of mathematics In some test thee ae mistakes that indicate the defectiveness in the udiments of mathematics. ~ Defectiveness of making algoithm 5. MISTAKES IN COUNTING THE INTEGER PART Most of the students (7) use algoithm to count the intege pat. Occuing mistakes: 5.. The student applies the algoithm popely, counts coectly, but the esult o the pat of the esult is wong The student chooses good algoithm, applies it well, counts coectly but does less division than equied The student chooses good algoithm, but unable to execute it coectly. He o she confounds the place of the quotient o the esiduum in the same execise seveal times.

6 5.4. He o she ties to use the algoithm in the execise 2. based on the decimal values of the decimal numeical system o the numeical system of based thiteen The student does not use the algoithm acquied. He o she divides the intege pat by 3 and chooses the quotient and esiduum as esults. 6. MISTAKES IN COUNTING THE FRACTION PART 6.. The student chooses good algoithm, uses the algoithm well, counts well, intepets the esult badly He o she puts the faction point at the wong place in the poduct He o she counts with the intege pat in the multiplications He o she uses the same algoithm (divisions) fo counting the factional pat and the intege pat The student wites down the following elation: = 0.abc = a 3 + b c He o she multiplies by 3 o 3 by tuns The multiplication is good, but the taking down is wong The student counts the factional pat with the algoithm used in the execise THE REASONS OF FAILURES 7.. Thei pevious mathematical knowledge is impefect The students poblem-solving and algoithm using ability is in low level Thee is a big diffeence between the abstaction level of the new and the pevious knowledge One lectue a week is not enough to pactise the empiical execises beside the theoy Pobably the leaning methods of the students ae not convenient The students do the algoithms mechanically and unable to intepet the esults They ae not familia enough with the algoithm o the way the algoithm is witten down is embaassing because it is diffeent fom the common fom of the division o the multiplication. 8. REFERENCES [2] Knuth: At of Compute Pogamming, Volume Műszaki Könyvkiadó Budapest. [] D. Váteész Magda: Matematikai pogamozás (főiskolai jegyzet)

Motithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100

Motithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100 Motithang Highe Seconday School Thimphu Thomde Mid Tem Examination 016 Subject: Mathematics Full Maks: 100 Class: IX Witing Time: 3 Hous Read the following instuctions caefully In this pape, thee ae thee

More information

F-IF Logistic Growth Model, Abstract Version

F-IF Logistic Growth Model, Abstract Version F-IF Logistic Gowth Model, Abstact Vesion Alignments to Content Standads: F-IFB4 Task An impotant example of a model often used in biology o ecology to model population gowth is called the logistic gowth

More information

Stanford University CS259Q: Quantum Computing Handout 8 Luca Trevisan October 18, 2012

Stanford University CS259Q: Quantum Computing Handout 8 Luca Trevisan October 18, 2012 Stanfod Univesity CS59Q: Quantum Computing Handout 8 Luca Tevisan Octobe 8, 0 Lectue 8 In which we use the quantum Fouie tansfom to solve the peiod-finding poblem. The Peiod Finding Poblem Let f : {0,...,

More information

4/18/2005. Statistical Learning Theory

4/18/2005. Statistical Learning Theory Statistical Leaning Theoy Statistical Leaning Theoy A model of supevised leaning consists of: a Envionment - Supplying a vecto x with a fixed but unknown pdf F x (x b Teache. It povides a desied esponse

More information

Circular Orbits. and g =

Circular Orbits. and g = using analyse planetay and satellite motion modelled as unifom cicula motion in a univesal gavitation field, a = v = 4π and g = T GM1 GM and F = 1M SATELLITES IN OBIT A satellite is any object that is

More information

ITI Introduction to Computing II

ITI Introduction to Computing II ITI 1121. Intoduction to Computing II Macel Tucotte School of Electical Engineeing and Compute Science Abstact data type: Stack Stack-based algoithms Vesion of Febuay 2, 2013 Abstact These lectue notes

More information

Current Balance Warm Up

Current Balance Warm Up PHYSICS EXPERIMENTS 133 Cuent Balance-1 Cuent Balance Wam Up 1. Foce between cuent-caying wies Wie 1 has a length L (whee L is "long") and caies a cuent I 0. What is the magnitude of the magnetic field

More information

A Bijective Approach to the Permutational Power of a Priority Queue

A Bijective Approach to the Permutational Power of a Priority Queue A Bijective Appoach to the Pemutational Powe of a Pioity Queue Ia M. Gessel Kuang-Yeh Wang Depatment of Mathematics Bandeis Univesity Waltham, MA 02254-9110 Abstact A pioity queue tansfoms an input pemutation

More information

DonnishJournals

DonnishJournals DonnishJounals 041-1189 Donnish Jounal of Educational Reseach and Reviews. Vol 1(1) pp. 01-017 Novembe, 014. http:///dje Copyight 014 Donnish Jounals Oiginal Reseach Pape Vecto Analysis Using MAXIMA Savaş

More information

New problems in universal algebraic geometry illustrated by boolean equations

New problems in universal algebraic geometry illustrated by boolean equations New poblems in univesal algebaic geomety illustated by boolean equations axiv:1611.00152v2 [math.ra] 25 Nov 2016 Atem N. Shevlyakov Novembe 28, 2016 Abstact We discuss new poblems in univesal algebaic

More information

Auchmuty High School Mathematics Department Advanced Higher Notes Teacher Version

Auchmuty High School Mathematics Department Advanced Higher Notes Teacher Version The Binomial Theoem Factoials Auchmuty High School Mathematics Depatment The calculations,, 6 etc. often appea in mathematics. They ae called factoials and have been given the notation n!. e.g. 6! 6!!!!!

More information

Physics 521. Math Review SCIENTIFIC NOTATION SIGNIFICANT FIGURES. Rules for Significant Figures

Physics 521. Math Review SCIENTIFIC NOTATION SIGNIFICANT FIGURES. Rules for Significant Figures Physics 51 Math Review SCIENIFIC NOAION Scientific Notation is based on exponential notation (whee decimal places ae expessed as a powe of 10). he numeical pat of the measuement is expessed as a numbe

More information

THE NUMBER OF TWO CONSECUTIVE SUCCESSES IN A HOPPE-PÓLYA URN

THE NUMBER OF TWO CONSECUTIVE SUCCESSES IN A HOPPE-PÓLYA URN TH NUMBR OF TWO CONSCUTIV SUCCSSS IN A HOPP-PÓLYA URN LARS HOLST Depatment of Mathematics, Royal Institute of Technology S 100 44 Stocholm, Sweden -mail: lholst@math.th.se Novembe 27, 2007 Abstact In a

More information

1) (A B) = A B ( ) 2) A B = A. i) A A = φ i j. ii) Additional Important Properties of Sets. De Morgan s Theorems :

1) (A B) = A B ( ) 2) A B = A. i) A A = φ i j. ii) Additional Important Properties of Sets. De Morgan s Theorems : Additional Impotant Popeties of Sets De Mogan s Theoems : A A S S Φ, Φ S _ ( A ) A ) (A B) A B ( ) 2) A B A B Cadinality of A, A, is defined as the numbe of elements in the set A. {a,b,c} 3, { }, while

More information

ON INDEPENDENT SETS IN PURELY ATOMIC PROBABILITY SPACES WITH GEOMETRIC DISTRIBUTION. 1. Introduction. 1 r r. r k for every set E A, E \ {0},

ON INDEPENDENT SETS IN PURELY ATOMIC PROBABILITY SPACES WITH GEOMETRIC DISTRIBUTION. 1. Introduction. 1 r r. r k for every set E A, E \ {0}, ON INDEPENDENT SETS IN PURELY ATOMIC PROBABILITY SPACES WITH GEOMETRIC DISTRIBUTION E. J. IONASCU and A. A. STANCU Abstact. We ae inteested in constucting concete independent events in puely atomic pobability

More information

Introduction Common Divisors. Discrete Mathematics Andrei Bulatov

Introduction Common Divisors. Discrete Mathematics Andrei Bulatov Intoduction Common Divisos Discete Mathematics Andei Bulatov Discete Mathematics Common Divisos 3- Pevious Lectue Integes Division, popeties of divisibility The division algoithm Repesentation of numbes

More information

EXAM NMR (8N090) November , am

EXAM NMR (8N090) November , am EXA NR (8N9) Novembe 5 9, 9. 1. am Remaks: 1. The exam consists of 8 questions, each with 3 pats.. Each question yields the same amount of points. 3. You ae allowed to use the fomula sheet which has been

More information

PDF Created with deskpdf PDF Writer - Trial ::

PDF Created with deskpdf PDF Writer - Trial :: A APPENDIX D TRIGONOMETRY Licensed to: jsamuels@bmcc.cun.edu PDF Ceated with deskpdf PDF Wite - Tial :: http://www.docudesk.com D T i g o n o m e t FIGURE a A n g l e s Angles can be measued in degees

More information

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights

More information

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to

More information

Pulse Neutron Neutron (PNN) tool logging for porosity Some theoretical aspects

Pulse Neutron Neutron (PNN) tool logging for porosity Some theoretical aspects Pulse Neuton Neuton (PNN) tool logging fo poosity Some theoetical aspects Intoduction Pehaps the most citicism of Pulse Neuton Neuon (PNN) logging methods has been chage that PNN is to sensitive to the

More information

Markscheme May 2017 Calculus Higher level Paper 3

Markscheme May 2017 Calculus Higher level Paper 3 M7/5/MATHL/HP3/ENG/TZ0/SE/M Makscheme May 07 Calculus Highe level Pape 3 pages M7/5/MATHL/HP3/ENG/TZ0/SE/M This makscheme is the popety of the Intenational Baccalaueate and must not be epoduced o distibuted

More information

MATHEMATICS GRADE 12 SESSION 38 (LEARNER NOTES)

MATHEMATICS GRADE 12 SESSION 38 (LEARNER NOTES) EXAM PREPARATION PAPER (A) Leane Note: In this session you will be given the oppotunity to wok on a past examination pape (Feb/Ma 010 DoE Pape ). The pape consists of 1 questions. Question 1, and will

More information

A STUDY OF HAMMING CODES AS ERROR CORRECTING CODES

A STUDY OF HAMMING CODES AS ERROR CORRECTING CODES AGU Intenational Jounal of Science and Technology A STUDY OF HAMMING CODES AS ERROR CORRECTING CODES Ritu Ahuja Depatment of Mathematics Khalsa College fo Women, Civil Lines, Ludhiana-141001, Punjab, (India)

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation

More information

3.1 Random variables

3.1 Random variables 3 Chapte III Random Vaiables 3 Random vaiables A sample space S may be difficult to descibe if the elements of S ae not numbes discuss how we can use a ule by which an element s of S may be associated

More information

Topic 4a Introduction to Root Finding & Bracketing Methods

Topic 4a Introduction to Root Finding & Bracketing Methods /8/18 Couse Instucto D. Raymond C. Rumpf Office: A 337 Phone: (915) 747 6958 E Mail: cumpf@utep.edu Topic 4a Intoduction to Root Finding & Backeting Methods EE 4386/531 Computational Methods in EE Outline

More information

Duality between Statical and Kinematical Engineering Systems

Duality between Statical and Kinematical Engineering Systems Pape 00, Civil-Comp Ltd., Stiling, Scotland Poceedings of the Sixth Intenational Confeence on Computational Stuctues Technology, B.H.V. Topping and Z. Bittna (Editos), Civil-Comp Pess, Stiling, Scotland.

More information

Probablistically Checkable Proofs

Probablistically Checkable Proofs Lectue 12 Pobablistically Checkable Poofs May 13, 2004 Lectue: Paul Beame Notes: Chis Re 12.1 Pobablisitically Checkable Poofs Oveview We know that IP = PSPACE. This means thee is an inteactive potocol

More information

Solution to HW 3, Ma 1a Fall 2016

Solution to HW 3, Ma 1a Fall 2016 Solution to HW 3, Ma a Fall 206 Section 2. Execise 2: Let C be a subset of the eal numbes consisting of those eal numbes x having the popety that evey digit in the decimal expansion of x is, 3, 5, o 7.

More information

Online-routing on the butterfly network: probabilistic analysis

Online-routing on the butterfly network: probabilistic analysis Online-outing on the buttefly netwok: obabilistic analysis Andey Gubichev 19.09.008 Contents 1 Intoduction: definitions 1 Aveage case behavio of the geedy algoithm 3.1 Bounds on congestion................................

More information

QIP Course 10: Quantum Factorization Algorithm (Part 3)

QIP Course 10: Quantum Factorization Algorithm (Part 3) QIP Couse 10: Quantum Factoization Algoithm (Pat 3 Ryutaoh Matsumoto Nagoya Univesity, Japan Send you comments to yutaoh.matsumoto@nagoya-u.jp Septembe 2018 @ Tokyo Tech. Matsumoto (Nagoya U. QIP Couse

More information

Berkeley Math Circle AIME Preparation March 5, 2013

Berkeley Math Circle AIME Preparation March 5, 2013 Algeba Toolkit Rules of Thumb. Make sue that you can pove all fomulas you use. This is even bette than memoizing the fomulas. Although it is best to memoize, as well. Stive fo elegant, economical methods.

More information

EM Boundary Value Problems

EM Boundary Value Problems EM Bounday Value Poblems 10/ 9 11/ By Ilekta chistidi & Lee, Seung-Hyun A. Geneal Desciption : Maxwell Equations & Loentz Foce We want to find the equations of motion of chaged paticles. The way to do

More information

Physics 2A Chapter 10 - Moment of Inertia Fall 2018

Physics 2A Chapter 10 - Moment of Inertia Fall 2018 Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.

More information

Motion in One Dimension

Motion in One Dimension Motion in One Dimension Intoduction: In this lab, you will investigate the motion of a olling cat as it tavels in a staight line. Although this setup may seem ovesimplified, you will soon see that a detailed

More information

1. Show that the volume of the solid shown can be represented by the polynomial 6x x.

1. Show that the volume of the solid shown can be represented by the polynomial 6x x. 7.3 Dividing Polynomials by Monomials Focus on Afte this lesson, you will be able to divide a polynomial by a monomial Mateials algeba tiles When you ae buying a fish tank, the size of the tank depends

More information

When two numbers are written as the product of their prime factors, they are in factored form.

When two numbers are written as the product of their prime factors, they are in factored form. 10 1 Study Guide Pages 420 425 Factos Because 3 4 12, we say that 3 and 4 ae factos of 12. In othe wods, factos ae the numbes you multiply to get a poduct. Since 2 6 12, 2 and 6 ae also factos of 12. The

More information

AP Physics C: Electricity and Magnetism 2001 Scoring Guidelines

AP Physics C: Electricity and Magnetism 2001 Scoring Guidelines AP Physics C: Electicity and Magnetism 1 Scoing Guidelines The mateials included in these files ae intended fo non-commecial use by AP teaches fo couse and exam pepaation; pemission fo any othe use must

More information

The Substring Search Problem

The Substring Search Problem The Substing Seach Poblem One algoithm which is used in a vaiety of applications is the family of substing seach algoithms. These algoithms allow a use to detemine if, given two chaacte stings, one is

More information

Psychometric Methods: Theory into Practice Larry R. Price

Psychometric Methods: Theory into Practice Larry R. Price ERRATA Psychometic Methods: Theoy into Pactice Lay R. Pice Eos wee made in Equations 3.5a and 3.5b, Figue 3., equations and text on pages 76 80, and Table 9.1. Vesions of the elevant pages that include

More information

As is natural, our Aerospace Structures will be described in a Euclidean three-dimensional space R 3.

As is natural, our Aerospace Structures will be described in a Euclidean three-dimensional space R 3. Appendix A Vecto Algeba As is natual, ou Aeospace Stuctues will be descibed in a Euclidean thee-dimensional space R 3. A.1 Vectos A vecto is used to epesent quantities that have both magnitude and diection.

More information

16 Modeling a Language by a Markov Process

16 Modeling a Language by a Markov Process K. Pommeening, Language Statistics 80 16 Modeling a Language by a Makov Pocess Fo deiving theoetical esults a common model of language is the intepetation of texts as esults of Makov pocesses. This model

More information

AP Physics C: Electricity and Magnetism 2003 Scoring Guidelines

AP Physics C: Electricity and Magnetism 2003 Scoring Guidelines AP Physics C: Electicity and Magnetism 3 Scoing Guidelines The mateials included in these files ae intended fo use by AP teaches fo couse and exam pepaation; pemission fo any othe use must be sought fom

More information

A New Approach to General Relativity

A New Approach to General Relativity Apeion, Vol. 14, No. 3, July 7 7 A New Appoach to Geneal Relativity Ali Rıza Şahin Gaziosmanpaşa, Istanbul Tukey E-mail: aizasahin@gmail.com Hee we pesent a new point of view fo geneal elativity and/o

More information

THE JEU DE TAQUIN ON THE SHIFTED RIM HOOK TABLEAUX. Jaejin Lee

THE JEU DE TAQUIN ON THE SHIFTED RIM HOOK TABLEAUX. Jaejin Lee Koean J. Math. 23 (2015), No. 3, pp. 427 438 http://dx.doi.og/10.11568/kjm.2015.23.3.427 THE JEU DE TAQUIN ON THE SHIFTED RIM HOOK TABLEAUX Jaejin Lee Abstact. The Schensted algoithm fist descibed by Robinson

More information

CALCULUS II Vectors. Paul Dawkins

CALCULUS II Vectors. Paul Dawkins CALCULUS II Vectos Paul Dawkins Table of Contents Peface... ii Vectos... 3 Intoduction... 3 Vectos The Basics... 4 Vecto Aithmetic... 8 Dot Poduct... 13 Coss Poduct... 21 2007 Paul Dawkins i http://tutoial.math.lama.edu/tems.aspx

More information

6 PROBABILITY GENERATING FUNCTIONS

6 PROBABILITY GENERATING FUNCTIONS 6 PROBABILITY GENERATING FUNCTIONS Cetain deivations pesented in this couse have been somewhat heavy on algeba. Fo example, detemining the expectation of the Binomial distibution (page 5.1 tuned out to

More information

KR- 21 FOR FORMULA SCORED TESTS WITH. Robert L. Linn, Robert F. Boldt, Ronald L. Flaugher, and Donald A. Rock

KR- 21 FOR FORMULA SCORED TESTS WITH. Robert L. Linn, Robert F. Boldt, Ronald L. Flaugher, and Donald A. Rock RB-66-4D ~ E S [ B A U R L C L Ii E TI KR- 21 FOR FORMULA SCORED TESTS WITH OMITS SCORED AS WRONG Robet L. Linn, Robet F. Boldt, Ronald L. Flaughe, and Donald A. Rock N This Bulletin is a daft fo inteoffice

More information

2.5 The Quarter-Wave Transformer

2.5 The Quarter-Wave Transformer /3/5 _5 The Quate Wave Tansfome /.5 The Quate-Wave Tansfome Reading Assignment: pp. 73-76 By now you ve noticed that a quate-wave length of tansmission line ( λ 4, β π ) appeas often in micowave engineeing

More information

Section 8.2 Polar Coordinates

Section 8.2 Polar Coordinates Section 8. Pola Coodinates 467 Section 8. Pola Coodinates The coodinate system we ae most familia with is called the Catesian coodinate system, a ectangula plane divided into fou quadants by the hoizontal

More information

Truncated Squarers with Constant and Variable Correction

Truncated Squarers with Constant and Variable Correction Please veify that ) all pages ae pesent, 2) all figues ae acceptable, 3) all fonts and special chaactes ae coect, and ) all text and figues fit within the Tuncated Squaes with Constant and Vaiable Coection

More information

ASTR415: Problem Set #6

ASTR415: Problem Set #6 ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal

More information

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007 School of Electical and Compute Engineeing, Conell Univesity ECE 303: Electomagnetic Fields and Waves Fall 007 Homewok 8 Due on Oct. 19, 007 by 5:00 PM Reading Assignments: i) Review the lectue notes.

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.07: Electromagnetism II September 15, 2012 Prof. Alan Guth PROBLEM SET 2

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.07: Electromagnetism II September 15, 2012 Prof. Alan Guth PROBLEM SET 2 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Depatment Physics 8.07: Electomagnetism II Septembe 5, 202 Pof. Alan Guth PROBLEM SET 2 DUE DATE: Monday, Septembe 24, 202. Eithe hand it in at the lectue,

More information

A generalization of the Bernstein polynomials

A generalization of the Bernstein polynomials A genealization of the Benstein polynomials Halil Ouç and Geoge M Phillips Mathematical Institute, Univesity of St Andews, Noth Haugh, St Andews, Fife KY16 9SS, Scotland Dedicated to Philip J Davis This

More information

High precision computer simulation of cyclotrons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D.

High precision computer simulation of cyclotrons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D. High pecision compute simulation of cyclotons KARAMYSHEVA T., AMIRKHANOV I. MALININ V., POPOV D. Abstact Effective and accuate compute simulations ae highly impotant in acceleatos design and poduction.

More information

10/04/18. P [P(x)] 1 negl(n).

10/04/18. P [P(x)] 1 negl(n). Mastemath, Sping 208 Into to Lattice lgs & Cypto Lectue 0 0/04/8 Lectues: D. Dadush, L. Ducas Scibe: K. de Boe Intoduction In this lectue, we will teat two main pats. Duing the fist pat we continue the

More information

Chapter 5 Linear Equations: Basic Theory and Practice

Chapter 5 Linear Equations: Basic Theory and Practice Chapte 5 inea Equations: Basic Theoy and actice In this chapte and the next, we ae inteested in the linea algebaic equation AX = b, (5-1) whee A is an m n matix, X is an n 1 vecto to be solved fo, and

More information

A Deep Convolutional Neural Network Based on Nested Residue Number System

A Deep Convolutional Neural Network Based on Nested Residue Number System A Deep Convolutional Neual Netwok Based on Nested Residue Numbe System Hioki Nakahaa Ehime Univesity, Japan Tsutomu Sasao Meiji Univesity, Japan Abstact A pe-tained deep convolutional neual netwok (DCNN)

More information

Chapter 3: Theory of Modular Arithmetic 38

Chapter 3: Theory of Modular Arithmetic 38 Chapte 3: Theoy of Modula Aithmetic 38 Section D Chinese Remainde Theoem By the end of this section you will be able to pove the Chinese Remainde Theoem apply this theoem to solve simultaneous linea conguences

More information

Physics 211: Newton s Second Law

Physics 211: Newton s Second Law Physics 211: Newton s Second Law Reading Assignment: Chapte 5, Sections 5-9 Chapte 6, Section 2-3 Si Isaac Newton Bon: Januay 4, 1643 Died: Mach 31, 1727 Intoduction: Kinematics is the study of how objects

More information

EN40: Dynamics and Vibrations. Midterm Examination Thursday March

EN40: Dynamics and Vibrations. Midterm Examination Thursday March EN40: Dynamics and Vibations Midtem Examination Thusday Mach 9 2017 School of Engineeing Bown Univesity NAME: Geneal Instuctions No collaboation of any kind is pemitted on this examination. You may bing

More information

Chapter 2: Introduction to Implicit Equations

Chapter 2: Introduction to Implicit Equations Habeman MTH 11 Section V: Paametic and Implicit Equations Chapte : Intoduction to Implicit Equations When we descibe cuves on the coodinate plane with algebaic equations, we can define the elationship

More information

MAGNETIC FIELD AROUND TWO SEPARATED MAGNETIZING COILS

MAGNETIC FIELD AROUND TWO SEPARATED MAGNETIZING COILS The 8 th Intenational Confeence of the Slovenian Society fo Non-Destuctive Testing»pplication of Contempoay Non-Destuctive Testing in Engineeing«Septembe 1-3, 5, Potoož, Slovenia, pp. 17-1 MGNETIC FIELD

More information

Preamble: Mind your language

Preamble: Mind your language Peamble: Mind you language The idiom of this Physics couse will be a mixtue of natual language and algebaic fomalism equiing a cetain attention. So, teat you algeba with the same espect that you offe to

More information

5.61 Physical Chemistry Lecture #23 page 1 MANY ELECTRON ATOMS

5.61 Physical Chemistry Lecture #23 page 1 MANY ELECTRON ATOMS 5.6 Physical Chemisty Lectue #3 page MAY ELECTRO ATOMS At this point, we see that quantum mechanics allows us to undestand the helium atom, at least qualitatively. What about atoms with moe than two electons,

More information

Encapsulation theory: the transformation equations of absolute information hiding.

Encapsulation theory: the transformation equations of absolute information hiding. 1 Encapsulation theoy: the tansfomation equations of absolute infomation hiding. Edmund Kiwan * www.edmundkiwan.com Abstact This pape descibes how the potential coupling of a set vaies as the set is tansfomed,

More information

AQI: Advanced Quantum Information Lecture 2 (Module 4): Order finding and factoring algorithms February 20, 2013

AQI: Advanced Quantum Information Lecture 2 (Module 4): Order finding and factoring algorithms February 20, 2013 AQI: Advanced Quantum Infomation Lectue 2 (Module 4): Ode finding and factoing algoithms Febuay 20, 203 Lectue: D. Mak Tame (email: m.tame@impeial.ac.uk) Intoduction In the last lectue we looked at the

More information

Lab #4: Newton s Second Law

Lab #4: Newton s Second Law Lab #4: Newton s Second Law Si Isaac Newton Reading Assignment: bon: Januay 4, 1643 Chapte 5 died: Mach 31, 1727 Chapte 9, Section 9-7 Intoduction: Potait of Isaac Newton by Si Godfey Knelle http://www.newton.cam.ac.uk/at/potait.html

More information

Chapter Eight Notes N P U1C8S4-6

Chapter Eight Notes N P U1C8S4-6 Chapte Eight Notes N P UC8S-6 Name Peiod Section 8.: Tigonometic Identities An identit is, b definition, an equation that is alwas tue thoughout its domain. B tue thoughout its domain, that is to sa that

More information

K.S.E.E.B., Malleshwaram, Bangalore SSLC Model Question Paper-1 (2015) Mathematics

K.S.E.E.B., Malleshwaram, Bangalore SSLC Model Question Paper-1 (2015) Mathematics K.S.E.E.B., Malleshwaam, Bangaloe SSLC Model Question Pape-1 (015) Mathematics Max Maks: 80 No. of Questions: 40 Time: Hous 45 minutes Code No. : 81E Fou altenatives ae given fo the each question. Choose

More information

Math Section 4.2 Radians, Arc Length, and Area of a Sector

Math Section 4.2 Radians, Arc Length, and Area of a Sector Math 1330 - Section 4. Radians, Ac Length, and Aea of a Secto The wod tigonomety comes fom two Geek oots, tigonon, meaning having thee sides, and mete, meaning measue. We have aleady defined the six basic

More information

A Crash Course in (2 2) Matrices

A Crash Course in (2 2) Matrices A Cash Couse in ( ) Matices Seveal weeks woth of matix algeba in an hou (Relax, we will only stuy the simplest case, that of matices) Review topics: What is a matix (pl matices)? A matix is a ectangula

More information

Relating Branching Program Size and. Formula Size over the Full Binary Basis. FB Informatik, LS II, Univ. Dortmund, Dortmund, Germany

Relating Branching Program Size and. Formula Size over the Full Binary Basis. FB Informatik, LS II, Univ. Dortmund, Dortmund, Germany Relating Banching Pogam Size and omula Size ove the ull Binay Basis Matin Saueho y Ingo Wegene y Ralph Wechne z y B Infomatik, LS II, Univ. Dotmund, 44 Dotmund, Gemany z ankfut, Gemany sauehof/wegene@ls.cs.uni-dotmund.de

More information

33. 12, or its reciprocal. or its negative.

33. 12, or its reciprocal. or its negative. Page 6 The Point is Measuement In spite of most of what has been said up to this point, we did not undetake this poject with the intent of building bette themometes. The point is to measue the peson. Because

More information

Using Laplace Transform to Evaluate Improper Integrals Chii-Huei Yu

Using Laplace Transform to Evaluate Improper Integrals Chii-Huei Yu Available at https://edupediapublicationsog/jounals Volume 3 Issue 4 Febuay 216 Using Laplace Tansfom to Evaluate Impope Integals Chii-Huei Yu Depatment of Infomation Technology, Nan Jeon Univesity of

More information

Revision of Lecture Eight

Revision of Lecture Eight Revision of Lectue Eight Baseband equivalent system and equiements of optimal tansmit and eceive filteing: (1) achieve zeo ISI, and () maximise the eceive SNR Thee detection schemes: Theshold detection

More information

Brief summary of functional analysis APPM 5440 Fall 2014 Applied Analysis

Brief summary of functional analysis APPM 5440 Fall 2014 Applied Analysis Bief summay of functional analysis APPM 5440 Fall 014 Applied Analysis Stephen Becke, stephen.becke@coloado.edu Standad theoems. When necessay, I used Royden s and Keyzsig s books as a efeence. Vesion

More information

Galilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O.

Galilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O. PHYS-2402 Chapte 2 Lectue 2 Special Relativity 1. Basic Ideas Sep. 1, 2016 Galilean Tansfomation vs E&M y K O z z y K In 1873, Maxwell fomulated Equations of Electomagnetism. v Maxwell s equations descibe

More information

Dynamic Visualization of Complex Integrals with Cabri II Plus

Dynamic Visualization of Complex Integrals with Cabri II Plus Dynamic Visualiation of omplex Integals with abi II Plus Sae MIKI Kawai-juu, IES Japan Email: sand_pictue@hotmailcom Abstact: Dynamic visualiation helps us undestand the concepts of mathematics This pape

More information

FUSE Fusion Utility Sequence Estimator

FUSE Fusion Utility Sequence Estimator FUSE Fusion Utility Sequence Estimato Belu V. Dasaathy Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500 belu.d@dynetics.com Sean D. Townsend Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500

More information

Surveillance Points in High Dimensional Spaces

Surveillance Points in High Dimensional Spaces Société de Calcul Mathématique SA Tools fo decision help since 995 Suveillance Points in High Dimensional Spaces by Benad Beauzamy Januay 06 Abstact Let us conside any compute softwae, elying upon a lage

More information

2 x 8 2 x 2 SKILLS Determine whether the given value is a solution of the. equation. (a) x 2 (b) x 4. (a) x 2 (b) x 4 (a) x 4 (b) x 8

2 x 8 2 x 2 SKILLS Determine whether the given value is a solution of the. equation. (a) x 2 (b) x 4. (a) x 2 (b) x 4 (a) x 4 (b) x 8 5 CHAPTER Fundamentals When solving equations that involve absolute values, we usually take cases. EXAMPLE An Absolute Value Equation Solve the equation 0 x 5 0 3. SOLUTION By the definition of absolute

More information

Fall 2014 Randomized Algorithms Oct 8, Lecture 3

Fall 2014 Randomized Algorithms Oct 8, Lecture 3 Fall 204 Randomized Algoithms Oct 8, 204 Lectue 3 Pof. Fiedich Eisenband Scibes: Floian Tamè In this lectue we will be concened with linea pogamming, in paticula Clakson s Las Vegas algoithm []. The main

More information

C/CS/Phys C191 Shor s order (period) finding algorithm and factoring 11/12/14 Fall 2014 Lecture 22

C/CS/Phys C191 Shor s order (period) finding algorithm and factoring 11/12/14 Fall 2014 Lecture 22 C/CS/Phys C9 Sho s ode (peiod) finding algoithm and factoing /2/4 Fall 204 Lectue 22 With a fast algoithm fo the uantum Fouie Tansfom in hand, it is clea that many useful applications should be possible.

More information

Math 301: The Erdős-Stone-Simonovitz Theorem and Extremal Numbers for Bipartite Graphs

Math 301: The Erdős-Stone-Simonovitz Theorem and Extremal Numbers for Bipartite Graphs Math 30: The Edős-Stone-Simonovitz Theoem and Extemal Numbes fo Bipatite Gaphs May Radcliffe The Edős-Stone-Simonovitz Theoem Recall, in class we poved Tuán s Gaph Theoem, namely Theoem Tuán s Theoem Let

More information

Phys 201A. Homework 5 Solutions

Phys 201A. Homework 5 Solutions Phys 201A Homewok 5 Solutions 3. In each of the thee cases, you can find the changes in the velocity vectos by adding the second vecto to the additive invese of the fist and dawing the esultant, and by

More information

Central Coverage Bayes Prediction Intervals for the Generalized Pareto Distribution

Central Coverage Bayes Prediction Intervals for the Generalized Pareto Distribution Statistics Reseach Lettes Vol. Iss., Novembe Cental Coveage Bayes Pediction Intevals fo the Genealized Paeto Distibution Gyan Pakash Depatment of Community Medicine S. N. Medical College, Aga, U. P., India

More information

arxiv: v1 [math.co] 1 Apr 2011

arxiv: v1 [math.co] 1 Apr 2011 Weight enumeation of codes fom finite spaces Relinde Juius Octobe 23, 2018 axiv:1104.0172v1 [math.co] 1 Ap 2011 Abstact We study the genealized and extended weight enumeato of the - ay Simplex code and

More information

Fast DCT-based image convolution algorithms and application to image resampling and hologram reconstruction

Fast DCT-based image convolution algorithms and application to image resampling and hologram reconstruction Fast DCT-based image convolution algoithms and application to image esampling and hologam econstuction Leonid Bilevich* a and Leonid Yaoslavsy** a a Depatment of Physical Electonics, Faculty of Engineeing,

More information

The Chromatic Villainy of Complete Multipartite Graphs

The Chromatic Villainy of Complete Multipartite Graphs Rocheste Institute of Technology RIT Schola Wos Theses Thesis/Dissetation Collections 8--08 The Chomatic Villainy of Complete Multipatite Gaphs Anna Raleigh an9@it.edu Follow this and additional wos at:

More information

Many Electron Atoms. Electrons can be put into approximate orbitals and the properties of the many electron systems can be catalogued

Many Electron Atoms. Electrons can be put into approximate orbitals and the properties of the many electron systems can be catalogued Many Electon Atoms The many body poblem cannot be solved analytically. We content ouselves with developing appoximate methods that can yield quite accuate esults (but usually equie a compute). The electons

More information

Trigonometry Standard Position and Radians

Trigonometry Standard Position and Radians MHF 4UI Unit 6 Day 1 Tigonomety Standad Position and Radians A. Standad Position of an Angle teminal am initial am Angle is in standad position when the initial am is the positive x-axis and the vetex

More information

COMPUTATIONS OF ELECTROMAGNETIC FIELDS RADIATED FROM COMPLEX LIGHTNING CHANNELS

COMPUTATIONS OF ELECTROMAGNETIC FIELDS RADIATED FROM COMPLEX LIGHTNING CHANNELS Pogess In Electomagnetics Reseach, PIER 73, 93 105, 2007 COMPUTATIONS OF ELECTROMAGNETIC FIELDS RADIATED FROM COMPLEX LIGHTNING CHANNELS T.-X. Song, Y.-H. Liu, and J.-M. Xiong School of Mechanical Engineeing

More information

Why Professor Richard Feynman was upset solving the Laplace equation for spherical waves? Anzor A. Khelashvili a)

Why Professor Richard Feynman was upset solving the Laplace equation for spherical waves? Anzor A. Khelashvili a) Why Pofesso Richad Feynman was upset solving the Laplace equation fo spheical waves? Anzo A. Khelashvili a) Institute of High Enegy Physics, Iv. Javakhishvili Tbilisi State Univesity, Univesity St. 9,

More information

2 Governing Equations

2 Governing Equations 2 Govening Equations This chapte develops the govening equations of motion fo a homogeneous isotopic elastic solid, using the linea thee-dimensional theoy of elasticity in cylindical coodinates. At fist,

More information

Introduction and Vectors

Introduction and Vectors SOLUTIONS TO PROBLEMS Intoduction and Vectos Section 1.1 Standads of Length, Mass, and Time *P1.4 Fo eithe sphee the volume is V = 4! and the mass is m =!V =! 4. We divide this equation fo the lage sphee

More information

CALCULATING THE NUMBER OF TWIN PRIMES WITH SPECIFIED DISTANCE BETWEEN THEM BASED ON THE SIMPLEST PROBABILISTIC MODEL

CALCULATING THE NUMBER OF TWIN PRIMES WITH SPECIFIED DISTANCE BETWEEN THEM BASED ON THE SIMPLEST PROBABILISTIC MODEL U.P.B. Sci. Bull. Seies A, Vol. 80, Iss.3, 018 ISSN 13-707 CALCULATING THE NUMBER OF TWIN PRIMES WITH SPECIFIED DISTANCE BETWEEN THEM BASED ON THE SIMPLEST PROBABILISTIC MODEL Sasengali ABDYMANAPOV 1,

More information

INTRODUCTION. 2. Vectors in Physics 1

INTRODUCTION. 2. Vectors in Physics 1 INTRODUCTION Vectos ae used in physics to extend the study of motion fom one dimension to two dimensions Vectos ae indispensable when a physical quantity has a diection associated with it As an example,

More information