ON WHAT BASIS ARE GRADUATE STUOH~TS

Size: px
Start display at page:

Download "ON WHAT BASIS ARE GRADUATE STUOH~TS"

Transcription

1 *-, 73. ON WHAT BASIS ARE GRADUATE STUOH~TS +** ; '6 USED I N TEACHING AND RESEARCH? A. N, Pearson UN I VERS t TY OF FLOR I DA In attacking t h i s problem, I am assuming that those in charge o f the program have decided that graduate work in meats i s desirable. It i s not my purpose t o defend t h i s stand, although I a m in agreement w i t h the committee in t h i s respect, but r a t h e r t o discuss the basis on which graduate students are used i n meats work. In attempting t o develop t h i s question, I wrote t o a number of you who I knev were d i r e c t i n g graduate work i n meats and asked for your viewpoints on the proper division between research and teaching, The number of r e s p o n ~ e s wa8 very p a t i m i n g and the comments have proven t o be extremely usef'ul in expanding t h i s t o p i c. Since we a r e a l l aware t h a t the graduate student i s probably the cheapest source of labor that can be obtained, there is a marked variation in h i s duties. Some of you have indicated that perhaps we take advantage of t h i s cheap source of labor as a means o f getting our j a n i t o r i a l eervices. Although i n some individual cases t h i s may prove t o be a handicap f o r the student, I a m sure that the majority of us a r e s t i l l saddled w i t h considerable j a n i t o r i a l duties and perhaps f e e l t h a t such t r a i n i n g w i l l be worthwhile, a t l e a s t i f we a r e t r a i n i n g future college meats men. Perhaps the most l o g i c a l answer as t o the proper division between teaching and research i s the old army stock Rnswer of "it a l l depends on the situation." I n other words, the division between teaching and research should depend upon w h a t we are training the student t o do when he completes hie graduate studies and what t r a i n i n g we a r e capable o f giving t h e student *om a standpoint of flacilities and staff assistance. Of these two factors, the training of the student f o r a s p e c i f i c 3013 ahould come first. Unfortunately, t h i s is much e a s i e r t o say than t o do, because we have never been capable of saying t h i s is the only Job t h a t you a r e capable of handling. I n autocratic countries, it is my understanding that we know w h a t our a t u r e position w i l l be, but as lorn as we have democracy, we can not be sure t h a t we are training our graduate students f o r t h e jobs that they w i l l take. Thus, o u r training must envelope a w i d e r f i e l d and prepare the graduate student for a s e r i e s of jobs rather than any single position. From t h i s do not take the view that I believe all students should receive the same t r a i n i n g, b u t on t h e contrary, it is my b e l i e f t h a t each student should be consulted as t o h i s m t u r e plans in order to b e s t determine h i s t r a i n i n g, both in rega,rd t o course work and research. It w i l l, of course, be necessary t o vary the t r a i n i n g so that the proper balance between research and teaching w i l l be achieved w i t h each individual graduate student. However, the point I want t o make i s that the graduate student desiring t o work f o r a meat packer may put much more of h i s time i n on research work of a technical nature than the graduate student intending t o operate a butcher shop. On the

2 74. other hand, I should l i k e t o r e i t e r a t e that we must neceasarily give the graduate student some experience i n both research and teaching i n order t o give him a broader understanding and t o increase h i s p o t e n t i a l f i e l d s o f employment. Naturally, the division between teaching and research may vary with the stage of t r a i n i n g t o which the student has progressed. For instance, t h e beginning student i s not qualified t o teach except as an a s s i s t a n t, b u t the advanced graduate student may be given complete charge of a laboratory section, a l e c t u r e section o r both. Similarly, the fyeedom that B graduate student i s capable of having i n the f i e l d of research must be determined by h i s major professor on a b a s i s of the students a b i l i t y and the stage of h i s t r a i n i n g. Frequently, it is not possible t o give the student the type of t r a i n i n g t h a t is needed because of poor f s c i l i t i e s and staff inadequaciee. Under such conditions, graduate atudents a r e often overloaded w i t h teaching r e s p o n s i b i l i t i e s and given too l i t t l e research experience except as he can work it i n t o an already f U L schedule of teaching. Thus, the research w i l l necessarily euffer and perhaps the student w i l l even lose i n t e r e s t i n h i s most basic training-the s b i l i t y t o carry out experiments and draw correct conclusions. It is especially important that research experience be gained under the good sound direction of a qualified researcher, since guidance is almoet if not e n t i r e l y lacking once the student completes h i s formal education. If we a r e unable t o give a student the training he desires because of i n s u f f i c i e n t h c i l l t i e a or too l i t t l e time t o devote t o directing h i s work, it i s b e s t that he be so informed. If a student s t i l l p e r s i s t s in doing work under such conditions, a t l e a s t he has been f'orewarned. Although no exact r u l e can be s e t up as t o the correct division of time between research and teaching, perhaps certain recommendations can be made. Before making any suggeetions, l e t uo assume they w i l l be applicable only t o the average student and not t o those, who msy be doing considerable teaching o r t o those having considerable a c t u a l research experience. Furthermore, since some student6 may be trying t o g e t t h e i r course work over before commencing t h e i r research work, any recommendations given would apply only t o those students on departmental appojntments as graduate a s s i s t a n t s or f e l LOWS Assuming that t h e student on an a8sistant6hip is required t o work a minimum, chances a r e he never heard of such short hours, of 20 hours per week, which we find required f o r the CorneLl graduate student appointments, no more than h a l f of the 20 hour minimum should be spent i n teaching. This means t h a t the student should not be aeeigned to asaist i n more than 2 three-hour laboratory periods per week and one l e c t u r e a week, which coupled with t h e time spent in preparation would e a s i l y require a minimum of 10 hours per week. Preferably, the amount oftlne spent i n teaching should consist of only one laboratory period per week, because too much time spent in teaching cause8 most students t o skip over t h e i r preparation and f a i l t o present t h e i r instructional work in a pleasing manner. This w i l l o f course neceesarily vary with the amount of research the etudent l e a c t i v e l y conducting, a13 there may be times when t h e teaching load can be varied in accordance w i t h the student's echedule of classes and h i s research program, Since it i s necessary for a l l graduate Student8 t o carry out some kind of a research project, a minlmwn o f 10 hours ehould be spent each week

3 75. conducting research. The reoearch program, o f course, need not be confined t o a c t u a l laboratory experiments, b u t can also include the necessary library work, a n a l y s i s of data and writing up the r e s u l t s. Naturally, the more w i l l i n g graduate students w i l l spend much more than the 10 required hours conducting research and as their problem advances w i l l, of course, f i n d more and more time is required t o keep the experiment going. It should be borne i n mind that a l l course work and studying connected w i t h course work 18 not acceptable under t h e c l a s e i f i c a t i o n s of e i t h e r research o r teaching. Although a minirmun of 20 hours is required between research and teaching, t h i s does not put any limit on the maximum amount of t i n a which m y be needed t o carry on the program. O f course, i f too much i e required e i t h e r under the heading of course work, research o r teaching, one o f t h e others is bound t o s u f f e r, so some euitable program must be worked out. A s far as t h e proper division between research and teaching is concerned i n the t r a i n i n g o f graduate students i n meats, t h e r e i s no hard and fast r u l e. Rather the division of time should depend upon the plans of the student f o r f i b r e employment, the a v a i l a b i l i t y o f f a c i l i t i e s and staff f o r i n s t r u c t i o n a l purposes and t h e stage of t r a i n i n g. A l l graduate Rtudents should be given 8ome experience in both teaching and rosearch in order t o develop the student i n both of these e s s e n t i a l f i e l d s, The plan f o r giving experience i n these f i e l d 6 should be f l e x i b l e enough t o permit changes a8 necessary to meet the individual's needs. The graduate student should not be used merely a8 a mean0 o f g e t t i n g teaching and research conducted, but r a t h e r under the c a r e & l supervision o f the major professor t h e graduate student should be t r a i n e d w i t h an eye t o h i s needs and stage of development. The best division of r e s p o n s i b i l i t y w i l l be t h e one which develops the s t u d e n t r e l a t e n t a b i l i t y i n both the f i e l d s o f research and teaching. CHAIRMAN AJXDERSON; This paper should i n c i t e considerable diecussion, and we have E. P. Margerum, Jr., o f Kansas S t a t e College. ME?. MARGERUM, JR.: Thank you, M r. Anderson. As Mr. Anderoon said, the subject matter o f Mr. Peareon's paper can be very controvereial. The problem o f handling o r guiding the graduate a s s i s t a n t is of'ten secondary only t o the labor secured from him. I t i s very much a personal problem, I doubt i f there are two men i n t h i s audience who t r e a t a graduate a s s i s t a n t i n exactly the same manner o r even approach the problem o f taking on a graduate assis.l;ant i n the same manner. The t i t l e o f M r. Pearson's paper, "On What BasiE: a r e Graduate Students Used i n Teaching and Research?" i s very often i n d i c a t i v e of the s i t u a t i o n i n which a gullible graduate a s s i s t a n t finds himself' upon a r r i v a l a t t h e i n s t i t u t i o n. Luckily I have never had t h e misfortune o f being "used" in the t r u e eense of the word, b u t I know that i n many i n s t i t u t i o n s the graduate a s s i s t a n t i s almost subservient t o the j a n i t o r. He is one l e v e l lower.

4 76. This afternoon Bob Bray had a very good idea, t h a t i s that t h e meats man a t t h e i n s t i t u t i o n should be the guiding influence f o r the graduate student o r even f o r the graduate a s s i s t a n t. If he f?ails i n that capacity, i f he fails t o be the guiding l i g h t, i f he fails t o rec r u i t another man for the meats f i e l d, then we have missed the boat and our work i s a l l t o naught. I r e a l i z e it i s often necessary t o be a Dutch uncle t o a graduate a s s i s t a n t. It is of'ten necessary t o be a prodder, i f you wish t o use t h a t word, puehing him forward, making him accomplish a l i t t l e more, b u t I think the most i d e a l a i t u a t i o n i s where the graduate assistant can be t r e a t e d as an equal o r as a co-worker. I would never advise the s i t u a t i o n where he f e e l s that he has a straw boss i n h i e major professor. tonight 1 Would a f e w o f you gentlemen c a r e t o argue over t h i o topic MR. WELLINGTON: Mr. Chairman, I think that maybe we are tending t o place too much emphasis on the a c t that the graduate a s s i s t a n t i s perhaps taken advantage of by the i n s t i t u t i o n. True, the graduate a s s i s t a n t s do a l o t of work. Most of us have had experience a t l e a s t on one end of t h a t s i t u a t i o n, and I think that the value the student receives *om t h i s work that he does c e r t a i n l y j u s t i f i e s a l l the encouragement t h a t he g e t s t o do the work, be it whatever form it may be. MR. MAIWERUM, JR.: thought as college hazing. T h a t g e t s back i n t o the same l i n e o f MR. BULL: M r, Chairman, I should l i k e t o ask Mr. Pearson when he talks about research does he mean research which he i s doing f o r the i n s t i t u t i o n o r f o r himself.. MR, PWSON: My answer t o t h a t would be that a l l research is f o r the i n s t i t u t i o n and f o r yourself, too, That is, it i s for the development of yourself and it i s also for. the i n s t i t u t i o n. MR. BULL: 1 w i l l agree that the research t h e graduate assista n t does, whether he does it for the i n s t i t u t i o n o r for himself, i s valua b l e t o him, b u t unfortunately when he does it f o r the i n s t i t u t i o n he does n o t get graduate c r e d i t f o r it. Most o f the graduate students a r e i n t e r e s t e d in c r e d i t. A t I l l i n o i s a half-time a s s i s t a n t is permitted t o take a degree course program in the graduate college. I f he teacheo he is supposed t o teach s i x c r e d i t hours a week unles there i s a laboratory connected with it. Then we f i g u r e it on a clock hour ba8is. Fellows do n o t do work f o r the University unless they do it f o r t h e i r own experience, which a good many of them do. I have had two o r three men who held fellowship6 who taught fop me in t h e feeding course taught for nothing simply because they wanted t o g e t the experience of teaching. But as far as time is concerned they do n o t do an axcessive amount of work. That is p a r t i c u l a r l y t r u e i n the summer time when they are permitted t o take a full-time graduate program. -- We do n o t ask them o r expect them t o do j a n i t o r work. do, they do it on t h e i r own without approval. If they

5 77. MR. W E R U M, JR.: PLk, '? # + f ;,, I should l i k e eo'4&ion the point t h a t you made that the graduate student does n o t receive c r e d i t f o r t h e research which he does f o r t h e i n s t i t u t i o n, I think there i s a bountiful source o f i n f o m t i o n and experience there f o r anyone who cares t o pick it up, and that although he cannot show it i n a t r a n s c r i p t as a d e f i n i t e hourly c r e d i t, he has something t h e r e that i s probably worth more than a c r e d i t on a t r a n s c r i p t. ~~ MR. MACIllIOTOSH: There is another item I t h i n k m i g h t be mentioned, and t h a t is t h e r e is sometimes a difference i n tho type o f appointment the student has. I n some cases those appointments a r e teachinz apsoinlments, and they a r e expected t o do teaching t o that amount, onef i f t h o r two-fifths o r one-half as the case may be. I n o t h e r case8 they a r e s t r i c t l y research a s s i s t a n t s and a r e expected t o do research work. It s o happens that ours a r e divided, but I could not quite get plr. Peareon's idea about t e n hours o f that amount of time t o pay for t h e individual t h e s i s. T h a t research you said i s h i s time on c r e d i t time, not on pay time. When he i s a s s i s t i n g w i t h reeearch he i s helping w i t h r e search project8 t h a t a r e being conducted not f o r h i s t h e s i s. It sometimes happens t o be a s i d e l i g h t which can be devoted t o h i s t h e s i s, but that i s a d d i t i o n a l time. MR. WANDERSTOCK: I j u s t wonder whether Mr. Pearson also feela that the graduate student should be c a l l e d upon t o do some exteneion work t o g e t t h a t experience. MR, PEARSON: I think you a r e adding more wood t o t h e fire t o c a l l upon him t o do exteneion work. There are only so many hours i n a week. He has a half-time appointment, and I put t h i a as t h e minimum, n o t as the maximum, you remember. Phese hours a r e minimum hours and n o t maximum hours and every etudent w i l l put i n much more than t h i s, that i s, assuming a forty-hour week, wkdchi a d is f o r graduate work, b u t he should devote not more than one-half of it t o a c t i v e teaching o f coursej I: r e a l i z e your point, Mr. Wckintosh, that some appointments a r e research appointments and some a r e teaching appointments, b u t we would go ahead and put the student on such a basis that he could be devoting a t least ten hours per week t o teaching and a t least ten hours per week t o research. That research may be other research, b u t it may a l s o be a portion o f h i s own research. The time is too l i m i t e d and i f he puts i n t e n hours per week f o r you and then i n addition he puts i n twenty hours per week f o r himself, besides putting i n twenty hours on your teaching and w h a t couroe work he has t o do he w i l l not get properly t r a i n e d. -- MR. MARGERUM, JR,: I want t o take issue w i t h you, Professor Pearson, i n that you said twenty hours a week, figuring that as h a l f of an average work week. Twenty hours devoted t o the college f o r h i s h a l f time s a l a r y. A minimum of ten hours, say, f o r ten c r e d i t a f o r h i e graduate c r e d i t s and research time f o r h i s t h e s i s, plus preparation f o r the c o l l e g i a t e requirements t o meet h i s p y ecale would p r e t t y much keep a man hopping. I do not think it i s possible t o reckon a graduate a s s i s t a n t ' s time i n a c t u a l hours, The most f e a s i b l e method of handling it i s t o come t o an agreement before he a r r i v e s a t the i n s t i t u t i o n and lay out a work program f o r him not so much i n hours as i n accomplishments.

6 78. MR. BRADY: I have certainly learned a l o t here. We a r e t a l k ing, but we c e r t a i n l y do not have the answers. I might mention that t h i s We t r y is w h a t we are doing w i t h folks who a r e working on t h e i r Ph.D's t o give them full-time appointments. We believe that is the l o g i c a l answer t o have more teaching and research experience. A l l o f their r e search t h e is on experiment station. It is a l l one deal w i t h us. We have two limitations. One is the Experiment Station Directorla o f f i c e e s t e e r between those two and it and the other is the graduate o f f i c e. W has worked out very w e l l. T h a t nearly tells us about where we can go on those who are working f o r t h e i r master's degreetx. They may be on a quarter t h e, half of which i s teaching and half o f which is research. W do not d r a w a l i n e. W e j u s t expect them t o work about sixteen hours a day and t o s l e e p about eight hours.. MR. PEARSON: I that is very well taken. dent regardless of how we they do not w o r r y about a t h i n k that Professor Brady has a point here That is, the end i s the t r a i n i n g of t h e s t u do it. A t Cornel1 they have a system whereby c r e d i t basis, that is, they do not Bay, "I got t e n hours because I put i n ten hours of reaearch." That i s not the basit3 02 it. The basis there, is that so much residence is a c t u a l l y required o f each student, that is, a c e r t a i n number o f terms in residence, and it is up t o the major professor t o determine where the balance l i e s. He could give you a l l research and it would n o t be necessary f o r you t o take even one course i f your committee decfded it was not neceesary. Residency is the only thing t h a t is required, I n other wordt3, the end is t r a i n i n g the graduate student. MR. BFUiTZLEZ: The question was raised here about how you a r e going t o divide t h i s research between w h a t belongs t o the man and what belongs t o the college. I do not know how that can be divided. It has alway8 been my impression t h a t on a research fellowship he j u s t does more o f it and gets c r e d i t f o r it whichever way he does it, whether he i s teaching or whether he is on full-time research. I do not see how in the world we can divide the research man does between w h a t belongs t o the college and w h a t he g e t s w e d i t f o r. MR, MARGERUM, JR,: As I said in the beginning, the u t i l i z a t i o n of graduate a s s i s t a n t s i n e i t h e r teaching o r research i s an individual problem, and we w i l l have t o meet the standards 'or the requirements o f the d i r e c t o r of the s t a t i o n as well a6 the graduate office. I f you can have a man eupposedly on a research a s s i s t a n t s h i p who can accomplish h i s own research project f o r h i e t h e s i s work, a t t h e 8ame time keeping the d i r e c t o r of the s t a t i o n happy why should anyone complain? A s long as everyone f e e l s that he i s benefiting from the s i t u ation, then I think a l l f a well and good. Is there any more discussion on the topic? I w i l l turn t h e C h a i r back t o M r. Anderson. Thank you. CHAIRMAN ANDERSON: The impression that I have got from the recent discussion is t h a t the Program Committee h i t upon a l i v e subject and the discussion t h a t followed has been worthwhile. I n order not t o delay our program tonight we w i l l take the next sub Sect here, "Experimental Design and Procedure Followed in Co-operating w i t h a Regional Beef Breeding Laboratory," and we have our good friend, Professor M. H. Hazaleus, from Colorado, t o present, ###

F A C I L C I I E S N E E D E D, N E A T S REOUIRED AND TCME N E C E S S A R Y FOR

F A C I L C I I E S N E E D E D, N E A T S REOUIRED AND TCME N E C E S S A R Y FOR 38, F A C I L C I I E S N E E D E D, N E A T S REOUIRED AND TCME N E C E S S A R Y FOR T E A C H I N G I D E N T I F I C A T I O N O f C U T S AND G R A D I N G NATHAN S. HALE U N I V E R S I T Y OF M

More information

Lecture - 24 Radial Basis Function Networks: Cover s Theorem

Lecture - 24 Radial Basis Function Networks: Cover s Theorem Neural Network and Applications Prof. S. Sengupta Department of Electronic and Electrical Communication Engineering Indian Institute of Technology, Kharagpur Lecture - 24 Radial Basis Function Networks:

More information

Hypothesis testing I. - In particular, we are talking about statistical hypotheses. [get everyone s finger length!] n =

Hypothesis testing I. - In particular, we are talking about statistical hypotheses. [get everyone s finger length!] n = Hypothesis testing I I. What is hypothesis testing? [Note we re temporarily bouncing around in the book a lot! Things will settle down again in a week or so] - Exactly what it says. We develop a hypothesis,

More information

(Refer Slide Time: 00:10)

(Refer Slide Time: 00:10) Chemical Reaction Engineering 1 (Homogeneous Reactors) Professor R. Krishnaiah Department of Chemical Engineering Indian Institute of Technology Madras Lecture No 10 Design of Batch Reactors Part 1 (Refer

More information

DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS Basic Concepts Paul Dawkins Table of Contents Preface... Basic Concepts... 1 Introduction... 1 Definitions... Direction Fields... 8 Final Thoughts...19 007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx

More information

METHODS FOR GRADING STUDENTS I N THE MEAT LABORATORY WORK

METHODS FOR GRADING STUDENTS I N THE MEAT LABORATORY WORK 86. METHODS FOR GRADING STUDENTS I N THE MEAT LABORATORY WORK The assignment of t h i s topic came very much as a surprise t o me, and as those I have questioned plead Innocent the mystery becomes even

More information

Algebra Exam. Solutions and Grading Guide

Algebra Exam. Solutions and Grading Guide Algebra Exam Solutions and Grading Guide You should use this grading guide to carefully grade your own exam, trying to be as objective as possible about what score the TAs would give your responses. Full

More information

Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay

Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Lecture - 6 Length Contraction and Time Dilation (Refer Slide Time: 00:29) In our last lecture,

More information

PART I. Performed by: Alexandra Jiménez

PART I. Performed by: Alexandra Jiménez PART I The beginning of this story takes place in Rota. Rota is a very small town in Spain. It is not far from the Bay of Cadiz. Rota is famous for its different kinds of fruit and vegetables. In particular,

More information

ED 357/358 - FIELD EXPERIENCE - LD & EI LESSON DESIGN & DELIVERY LESSON PLAN #4

ED 357/358 - FIELD EXPERIENCE - LD & EI LESSON DESIGN & DELIVERY LESSON PLAN #4 ED 357/358 - FIELD EXPERIENCE - LD & EI LESSON DESIGN & DELIVERY LESSON PLAN #4 Your Name: Sarah Lidgard School: Bentheim Elementary School Lesson: Telling Time Length: approx. 50 minutes Cooperating Teacher:

More information

Math 308 Midterm Answers and Comments July 18, Part A. Short answer questions

Math 308 Midterm Answers and Comments July 18, Part A. Short answer questions Math 308 Midterm Answers and Comments July 18, 2011 Part A. Short answer questions (1) Compute the determinant of the matrix a 3 3 1 1 2. 1 a 3 The determinant is 2a 2 12. Comments: Everyone seemed to

More information

Quadratic Equations Part I

Quadratic Equations Part I Quadratic Equations Part I Before proceeding with this section we should note that the topic of solving quadratic equations will be covered in two sections. This is done for the benefit of those viewing

More information

LECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield

LECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield LECSS Physics 11 Introduction to Physics and Math Methods 1 Physics 11 Introduction to Physics and Math Methods In this introduction, you will get a more in-depth overview of what Physics is, as well as

More information

Science Grade 01 Unit 07 Exemplar Lesson 02: Investigating the Moon, the Stars, and the Sky

Science Grade 01 Unit 07 Exemplar Lesson 02: Investigating the Moon, the Stars, and the Sky Grade 1 Unit: 07 Lesson: 02 Suggested Duration: 5 days Grade 01 Unit 07 Exemplar Lesson 02: Investigating the Moon, the Stars, and the Sky This lesson is one approach to teaching the State Standards associated

More information

SOLVING EQUATIONS AND DEVELOPING THE FOUNDATION FOR PROOFS

SOLVING EQUATIONS AND DEVELOPING THE FOUNDATION FOR PROOFS SOLVING EQUATIONS AND DEVELOPING THE FOUNDATION FOR PROOFS 6.EE.6 and 6.EE.7 CONTENTS The types of documents contained in the unit are listed below. Throughout the unit, the documents are arranged by lesson.

More information

Math 38: Graph Theory Spring 2004 Dartmouth College. On Writing Proofs. 1 Introduction. 2 Finding A Solution

Math 38: Graph Theory Spring 2004 Dartmouth College. On Writing Proofs. 1 Introduction. 2 Finding A Solution Math 38: Graph Theory Spring 2004 Dartmouth College 1 Introduction On Writing Proofs What constitutes a well-written proof? A simple but rather vague answer is that a well-written proof is both clear and

More information

One day an ant was drinking at a small stream and fell in. She made desperate

One day an ant was drinking at a small stream and fell in. She made desperate (A) One day an ant was drinking at a small stream and fell in. She made desperate efforts to reach the side, but made no progress at all. The poor ant almost exhausted was still bravely doing her best

More information

Amount of Substance and Its Unit Mole- Connecting the Invisible Micro World to the Observable Macro World Part 2 (English, mp4)

Amount of Substance and Its Unit Mole- Connecting the Invisible Micro World to the Observable Macro World Part 2 (English, mp4) Amount of Substance and Its Unit Mole- Connecting the Invisible Micro World to the Observable Macro World Part 2 (English, mp4) [MUSIC PLAYING] Instructor: Hi, everyone. Welcome back. I hope you had some

More information

18 : ( ( ( ( ( ( ( ( ( ( ( (3-4. (1. (2. (3. (4-5» «. (4 (3 (2

18 : ( ( ( ( ( ( ( ( ( ( ( (3-4. (1. (2. (3. (4-5» «. (4 (3 (2 1 1389-18 25 1 25 20 50 26 25 17 75 51 25 20 100 76 25 75 : 100 : 135 : 175 : 18 : - - - (2 - - - (4 - - - (2 - - - (4 - - - (2 - - - (4 - - - (1 - - - (3-2 - - - (1 - - - (3-3 - - - (1 - - - (3-4. (1.

More information

( )( b + c) = ab + ac, but it can also be ( )( a) = ba + ca. Let s use the distributive property on a couple of

( )( b + c) = ab + ac, but it can also be ( )( a) = ba + ca. Let s use the distributive property on a couple of Factoring Review for Algebra II The saddest thing about not doing well in Algebra II is that almost any math teacher can tell you going into it what s going to trip you up. One of the first things they

More information

Dream Jobs: Solar system ambassador

Dream Jobs: Solar system ambassador Dream Jobs: Solar system ambassador By NASA.gov, adapted by Newsela staff on 11.29.16 Word Count 869 Astronomer Derrick Pitts examines a telescope owned by Galileo Galilei that was on display at his museum,

More information

Instructor (Brad Osgood)

Instructor (Brad Osgood) TheFourierTransformAndItsApplications-Lecture26 Instructor (Brad Osgood): Relax, but no, no, no, the TV is on. It's time to hit the road. Time to rock and roll. We're going to now turn to our last topic

More information

Measuring Keepers S E S S I O N 1. 5 A

Measuring Keepers S E S S I O N 1. 5 A S E S S I O N 1. 5 A Measuring Keepers Math Focus Points Naming, notating, and telling time to the hour on a digital and an analog clock Understanding the meaning of at least in the context of linear measurement

More information

The topics in this section concern with the first course objective.

The topics in this section concern with the first course objective. 1.1 Systems & Probability The topics in this section concern with the first course objective. A system is one of the most fundamental concepts and one of the most useful and powerful tools in STEM (science,

More information

Squaring and Unsquaring

Squaring and Unsquaring PROBLEM STRINGS LESSON 8.1 Squaring and Unsquaring At a Glance (6 6)* ( 6 6)* (1 1)* ( 1 1)* = 64 17 = 64 + 15 = 64 ( + 3) = 49 ( 7) = 5 ( + ) + 1= 8 *optional problems Objectives The goal of this string

More information

Making the grade. by Chris Sangwin. Making the grade

Making the grade. by Chris Sangwin. Making the grade 1997 2009, Millennium Mathematics Project, University of Cambridge. Permission is granted to print and copy this page on paper for non commercial use. For other uses, including electronic redistribution,

More information

Introducing Proof 1. hsn.uk.net. Contents

Introducing Proof 1. hsn.uk.net. Contents Contents 1 1 Introduction 1 What is proof? 1 Statements, Definitions and Euler Diagrams 1 Statements 1 Definitions Our first proof Euler diagrams 4 3 Logical Connectives 5 Negation 6 Conjunction 7 Disjunction

More information

Solving with Absolute Value

Solving with Absolute Value Solving with Absolute Value Who knew two little lines could cause so much trouble? Ask someone to solve the equation 3x 2 = 7 and they ll say No problem! Add just two little lines, and ask them to solve

More information

Academic Affairs Assessment of Student Learning Report for Academic Year

Academic Affairs Assessment of Student Learning Report for Academic Year Academic Affairs Assessment of Student Learning Report for Academic Year 2017-2018. Department/Program Chemistry Assessment Coordinator s Name: Micheal Fultz Assessment Coordinator s Email Address: mfultz@wvstateu.edu

More information

Student Questionnaire (s) Main Survey

Student Questionnaire (s) Main Survey School: Class: Student: Identification Label IEA Third International Mathematics and Science Study - Repeat Student Questionnaire (s) Main Survey TIMSS Study Center Boston College Chestnut Hill, MA 02467

More information

Error Correcting Codes Prof. Dr. P Vijay Kumar Department of Electrical Communication Engineering Indian Institute of Science, Bangalore

Error Correcting Codes Prof. Dr. P Vijay Kumar Department of Electrical Communication Engineering Indian Institute of Science, Bangalore (Refer Slide Time: 00:54) Error Correcting Codes Prof. Dr. P Vijay Kumar Department of Electrical Communication Engineering Indian Institute of Science, Bangalore Lecture No. # 05 Cosets, Rings & Fields

More information

Featured Alumna Sarah Caudill ( 06)

Featured Alumna Sarah Caudill ( 06) Featured Alumna Sarah Caudill ( 06) As a high school student applying to colleges, I had a choice between Stetson and the University of Florida. I reasoned that I would receive a more personalized education

More information

Design and Optimization of Energy Systems Prof. C. Balaji Department of Mechanical Engineering Indian Institute of Technology, Madras

Design and Optimization of Energy Systems Prof. C. Balaji Department of Mechanical Engineering Indian Institute of Technology, Madras Design and Optimization of Energy Systems Prof. C. Balaji Department of Mechanical Engineering Indian Institute of Technology, Madras Lecture No. # 10 Convergence Characteristics of Newton-Raphson Method

More information

Practical Psychic Self-Defense: Understanding and Surviving Unseen Influences

Practical Psychic Self-Defense: Understanding and Surviving Unseen Influences Practical Psychic Self-Defense: Understanding and Surviving Unseen Influences Robert Bruce Click here if your download doesn"t start automatically Practical Psychic Self-Defense: Understanding and Surviving

More information

Chapter 13 - Inverse Functions

Chapter 13 - Inverse Functions Chapter 13 - Inverse Functions In the second part of this book on Calculus, we shall be devoting our study to another type of function, the exponential function and its close relative the Sine function.

More information

QUANTUM TOUCH BY RICHARD GORDON DOWNLOAD EBOOK : QUANTUM TOUCH BY RICHARD GORDON PDF

QUANTUM TOUCH BY RICHARD GORDON DOWNLOAD EBOOK : QUANTUM TOUCH BY RICHARD GORDON PDF Read Online and Download Ebook QUANTUM TOUCH BY RICHARD GORDON DOWNLOAD EBOOK : QUANTUM TOUCH BY RICHARD GORDON PDF Click link bellow and free register to download ebook: QUANTUM TOUCH BY RICHARD GORDON

More information

SPIRITUAL GIFTS. ( ) ( ) 1. Would you describe yourself as an effective public speaker?

SPIRITUAL GIFTS. ( ) ( ) 1. Would you describe yourself as an effective public speaker? SPIRITUAL GIFTS QUESTIONNAIRE: SPIRITUAL GIFTS ( ) ( ) 1. Would you describe yourself as an effective public speaker? ( ) ( ) 2. Do you find it easy and enjoyable to spend time in intense study and research

More information

Physics 162b Quantum Mechanics

Physics 162b Quantum Mechanics Physics 162b Quantum Mechanics Contact details and office hours Syllabus for Winter/Spring 2019 Instructor: Albion Lawrence. Contact info. Office: Abelson 344. Phone: 781-736-2865. Email: albion@brandeis.edu.

More information

CIMA Dates and Prices Online Classroom Live September August 2016

CIMA Dates and Prices Online Classroom Live September August 2016 CIMA Dates and Prices Online Classroom Live September 2015 - August 2016 This document provides detail of the programmes that are being offered for the Objective Tests and Integrated Case Study Exams from

More information

REVIEW OF THE EMERGING ISSUES TASK FORCE

REVIEW OF THE EMERGING ISSUES TASK FORCE REVIEW OF THE EMERGING ISSUES TASK FORCE Conclusions and Recommendations Financial Accounting Standards Board www.fasb.org REVIEW OF THE EMERGING ISSUES TASK FORCE BACKGROUND OF THE EITF The Financial

More information

FIREHOUSE MAGAZINE EMERGENCY VEHICLE OPERATIONS PERSONALLY OPERATED VEHICLES P.O.V. S KILL

FIREHOUSE MAGAZINE EMERGENCY VEHICLE OPERATIONS PERSONALLY OPERATED VEHICLES P.O.V. S KILL FIREHOUSE MAGAZINE EMERGENCY VEHICLE OPERATIONS PERSONALLY OPERATED VEHICLES P.O.V. S KILL Unfortunately there has been a steady increase in the number of firefighters killed behind the wheel of their

More information

Algebra. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.

Algebra. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. This document was written and copyrighted by Paul Dawkins. Use of this document and its online version is governed by the Terms and Conditions of Use located at. The online version of this document is

More information

The Celsius temperature scale is based on the freezing point and the boiling point of water. 12 degrees Celsius below zero would be written as

The Celsius temperature scale is based on the freezing point and the boiling point of water. 12 degrees Celsius below zero would be written as Prealgebra, Chapter 2 - Integers, Introductory Algebra 2.1 Integers In the real world, numbers are used to represent real things, such as the height of a building, the cost of a car, the temperature of

More information

Advanced Marine Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology Madras

Advanced Marine Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology Madras Advanced Marine Structures Prof. Dr. Srinivasan Chandrasekaran Department of Ocean Engineering Indian Institute of Technology Madras Lecture - 13 Ultimate Limit State - II We will now discuss the thirteenth

More information

Pig organ transplants within 5 years

Pig organ transplants within 5 years www.breaking News English.com Ready-to-use ESL / EFL Lessons Pig organ transplants within 5 years URL: http://www.breakingnewsenglish.com/0509/050911-xenotransplant.html Today s contents The Article 2

More information

The key is that there are two disjoint populations, and everyone in the market is on either one side or the other

The key is that there are two disjoint populations, and everyone in the market is on either one side or the other Econ 805 Advanced Micro Theory I Dan Quint Fall 2009 Lecture 17 So... two-sided matching markets. First off, sources. I ve updated the syllabus for the next few lectures. As always, most of the papers

More information

Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi

Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi Communication Engineering Prof. Surendra Prasad Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 41 Pulse Code Modulation (PCM) So, if you remember we have been talking

More information

Solving Equations by Adding and Subtracting

Solving Equations by Adding and Subtracting SECTION 2.1 Solving Equations by Adding and Subtracting 2.1 OBJECTIVES 1. Determine whether a given number is a solution for an equation 2. Use the addition property to solve equations 3. Determine whether

More information

Course Evaluation, FYTN04 Theoretical Particle. Particle Physics, Fall 11, Department of Astronomy and Theoretical Physics

Course Evaluation, FYTN04 Theoretical Particle. Particle Physics, Fall 11, Department of Astronomy and Theoretical Physics 1 of 16 03/07/2012 03:41 PM Course Evaluation, FYTN04 Theoretical Particle Physics, Fall 11, Department of Astronomy and Theoretical Physics Course Evaluation, FYTN04 Theoretical Particle Physics, Fall

More information

Fourth Grade News Flash

Fourth Grade News Flash S Fourth Grade News Flash November 8, 2013 Dates to Remember 11/4 - No School 11/8 - End of 1 st Trimester 11/13 and 11/14 - Family Breakfast 11/15 - Report Cards sent home Language Arts This week s selection

More information

To: Amanda From: Daddy Date: 2004 February 19 About: How to solve math problems

To: Amanda From: Daddy Date: 2004 February 19 About: How to solve math problems to Amanda p.1 To: Amanda From: Daddy Date: 2004 February 19 About: How to solve math problems There are 4 steps in solving the kind of math problem you showed me. I'll list the steps first, then explain

More information

Chemistry 883 Computational Quantum Chemistry

Chemistry 883 Computational Quantum Chemistry Chemistry 883 Computational Quantum Chemistry Instructor Contact Information Professor Benjamin G. Levine levine@chemistry.msu.edu 215 Chemistry Building 517-353-1113 Office Hours Tuesday 9:00-11:00 am

More information

Chemical Reaction Engineering Prof. JayantModak Department of Chemical Engineering Indian Institute of Science, Bangalore

Chemical Reaction Engineering Prof. JayantModak Department of Chemical Engineering Indian Institute of Science, Bangalore Chemical Reaction Engineering Prof. JayantModak Department of Chemical Engineering Indian Institute of Science, Bangalore Module No. #05 Lecture No. #29 Non Isothermal Reactor Operation Let us continue

More information

The elements that make up our bodies formed from the violent explosions of massive

The elements that make up our bodies formed from the violent explosions of massive Page 1 The elements that make up our bodies formed from the violent explosions of massive stars. The same shapes that we trace when we look up at the sky were marveled at centuries before us by the ancient

More information

Thermodynamics (Classical) for Biological Systems. Prof. G. K. Suraishkumar. Department of Biotechnology. Indian Institute of Technology Madras

Thermodynamics (Classical) for Biological Systems. Prof. G. K. Suraishkumar. Department of Biotechnology. Indian Institute of Technology Madras Thermodynamics (Classical) for Biological Systems Prof. G. K. Suraishkumar Department of Biotechnology Indian Institute of Technology Madras Module No. #04 Thermodynamics of solutions Lecture No. #22 Partial

More information

Serena: I don t think that works because if n is 20 and you do 6 less than that you get 20 6 = 14. I think we should write! 6 > 4

Serena: I don t think that works because if n is 20 and you do 6 less than that you get 20 6 = 14. I think we should write! 6 > 4 24 4.6 Taking Sides A Practice Understanding Task Joaquin and Serena work together productively in their math class. They both contribute their thinking and when they disagree, they both give their reasons

More information

Structure of Materials Prof. Anandh Subramaniam Department of Material Science and Engineering Indian Institute of Technology, Kanpur

Structure of Materials Prof. Anandh Subramaniam Department of Material Science and Engineering Indian Institute of Technology, Kanpur Structure of Materials Prof. Anandh Subramaniam Department of Material Science and Engineering Indian Institute of Technology, Kanpur Lecture - 5 Geometry of Crystals: Symmetry, Lattices The next question

More information

Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities

Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities These 2 lessons can easily be taught in 2 class periods. If you like these lessons, please consider using other Eureka lessons as well.

More information

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module - 4.3 Lecture - 24 Matrix Analysis of Structures with Axial Elements (Refer

More information

FRACTIONS Book 1 An Introduction to Fractions for the Adult Learner

FRACTIONS Book 1 An Introduction to Fractions for the Adult Learner ACADEMIC STUDIES MATH Support Materials and Exercises for FRACTIONS Book An Introduction to Fractions for the Adult Learner SPRING FRACTIONS Fractions are used in our everyday life. We talk about fractions

More information

7.6 Customary Units of Weight and Capacity

7.6 Customary Units of Weight and Capacity www.ck12.org Chapter 7. Multiplication and Division of Fractions 7.6 Customary Units of Weight and Capacity Introduction Weighing in on Animals Julie has decided that her favorite rainforest topic has

More information

Appendix A. Review of Basic Mathematical Operations. 22Introduction

Appendix A. Review of Basic Mathematical Operations. 22Introduction Appendix A Review of Basic Mathematical Operations I never did very well in math I could never seem to persuade the teacher that I hadn t meant my answers literally. Introduction Calvin Trillin Many of

More information

Rising Algebra 2/Trig Students!

Rising Algebra 2/Trig Students! Rising Algebra 2/Trig Students! As a 7 th grader entering in to Algebra 2/Trig next year, it is very important that you have mastered the topics listed below. The majority of the topics were taught in

More information

Probability and Independence Terri Bittner, Ph.D.

Probability and Independence Terri Bittner, Ph.D. Probability and Independence Terri Bittner, Ph.D. The concept of independence is often confusing for students. This brief paper will cover the basics, and will explain the difference between independent

More information

A Brief Introduction to Proofs

A Brief Introduction to Proofs A Brief Introduction to Proofs William J. Turner October, 010 1 Introduction Proofs are perhaps the very heart of mathematics. Unlike the other sciences, mathematics adds a final step to the familiar scientific

More information

Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur

Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur Lecture 02 Groups: Subgroups and homomorphism (Refer Slide Time: 00:13) We looked

More information

Error Correcting Codes Prof. Dr. P. Vijay Kumar Department of Electrical Communication Engineering Indian Institute of Science, Bangalore

Error Correcting Codes Prof. Dr. P. Vijay Kumar Department of Electrical Communication Engineering Indian Institute of Science, Bangalore (Refer Slide Time: 00:15) Error Correcting Codes Prof. Dr. P. Vijay Kumar Department of Electrical Communication Engineering Indian Institute of Science, Bangalore Lecture No. # 03 Mathematical Preliminaries:

More information

Circuits for Analog System Design Prof. Gunashekaran M K Center for Electronics Design and Technology Indian Institute of Science, Bangalore

Circuits for Analog System Design Prof. Gunashekaran M K Center for Electronics Design and Technology Indian Institute of Science, Bangalore Circuits for Analog System Design Prof. Gunashekaran M K Center for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture No. # 08 Temperature Indicator Design Using Op-amp Today,

More information

Atm Sci 360 Synoptic Meteorology I Lecture: TR 9:30-10:45a, EMS E423 Lab: W 2-3:50p, EMS W434 Fall 2014

Atm Sci 360 Synoptic Meteorology I Lecture: TR 9:30-10:45a, EMS E423 Lab: W 2-3:50p, EMS W434 Fall 2014 Atm Sci 360 Synoptic Meteorology I Lecture: TR 9:30-10:45a, EMS E423 Lab: W 2-3:50p, EMS W434 Fall 2014 Instructor: Prof. Clark Evans Contact: (414) 229-5116, evans36@uwm.edu, EMS E486 Office Hours: TR

More information

Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras. Lecture - 13 Conditional Convergence

Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras. Lecture - 13 Conditional Convergence Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras Lecture - 13 Conditional Convergence Now, there are a few things that are remaining in the discussion

More information

Water Resources Systems Prof. P. P. Mujumdar Department of Civil Engineering Indian Institute of Science, Bangalore

Water Resources Systems Prof. P. P. Mujumdar Department of Civil Engineering Indian Institute of Science, Bangalore Water Resources Systems Prof. P. P. Mujumdar Department of Civil Engineering Indian Institute of Science, Bangalore Module No. # 05 Lecture No. # 22 Reservoir Capacity using Linear Programming (2) Good

More information

Physicists' Epistemologies of Quantum Mechanics

Physicists' Epistemologies of Quantum Mechanics Physicists' Epistemologies of Quantum Mechanics Raymond A. Hodges Physics Education Research Group University of Maryland College Park AAPT Summer Meeting Madison, Wisconsin August 4, 2003 Supported in

More information

How to write maths (well)

How to write maths (well) How to write maths (well) Dr Euan Spence 29 September 2017 These are the slides from a talk I gave to the new first-year students at Bath, annotated with some of the things I said (which appear in boxes

More information

Biostatistics and Design of Experiments Prof. Mukesh Doble Department of Biotechnology Indian Institute of Technology, Madras

Biostatistics and Design of Experiments Prof. Mukesh Doble Department of Biotechnology Indian Institute of Technology, Madras Biostatistics and Design of Experiments Prof. Mukesh Doble Department of Biotechnology Indian Institute of Technology, Madras Lecture - 39 Regression Analysis Hello and welcome to the course on Biostatistics

More information

A REVIEW OF RADIO ASTRONOMY IN THE USA I. INTRODUCTION

A REVIEW OF RADIO ASTRONOMY IN THE USA I. INTRODUCTION A REVIEW OF RADIO ASTRONOMY IN THE USA I. INTRODUCTION It has been suggested that the present time would be opportune for a review to be made of the whole field of radio astronomy in the country. In this

More information

Chapter 9: Apportionment

Chapter 9: Apportionment Chapter 9: Apportionment Apportionment involves dividing something up, just like fair division. In fair division we are dividing objects among people while in apportionment we are dividing people among

More information

The Inductive Proof Template

The Inductive Proof Template CS103 Handout 24 Winter 2016 February 5, 2016 Guide to Inductive Proofs Induction gives a new way to prove results about natural numbers and discrete structures like games, puzzles, and graphs. All of

More information

1.1 Administrative Stuff

1.1 Administrative Stuff 601.433 / 601.633 Introduction to Algorithms Lecturer: Michael Dinitz Topic: Introduction, Karatsuba/Strassen Date: 9/4/18 1.1 Administrative Stuff Welcome to Algorithms! In this class you will learn the

More information

CS 124 Math Review Section January 29, 2018

CS 124 Math Review Section January 29, 2018 CS 124 Math Review Section CS 124 is more math intensive than most of the introductory courses in the department. You re going to need to be able to do two things: 1. Perform some clever calculations to

More information

Twin Case Study: Treatment for Articulation Disabilities

Twin Case Study: Treatment for Articulation Disabilities Twin Case Study: Treatment for Articulation Disabilities Sirius Qin and Jun Chen November 5, 010 Department of Statistics University of British Columbia For Angela Feehan M.Sc student Audiology and Speech

More information

Chapter 3 ALGEBRA. Overview. Algebra. 3.1 Linear Equations and Applications 3.2 More Linear Equations 3.3 Equations with Exponents. Section 3.

Chapter 3 ALGEBRA. Overview. Algebra. 3.1 Linear Equations and Applications 3.2 More Linear Equations 3.3 Equations with Exponents. Section 3. 4 Chapter 3 ALGEBRA Overview Algebra 3.1 Linear Equations and Applications 3.2 More Linear Equations 3.3 Equations with Exponents 5 LinearEquations 3+ what = 7? If you have come through arithmetic, the

More information

Answering Questions About Being a Professor by Bill Menke, January 16, 2016

Answering Questions About Being a Professor by Bill Menke, January 16, 2016 Answering Questions About Being a Professor by Bill Menke, January 16, 2016 A correspondent asks: Hello Mr. Menke! My name is Rashmina XXXXXX and I am a freshman in a high school in upstate New York. In

More information

Figure 1. Distance depends upon time.

Figure 1. Distance depends upon time. Section 3.1 Linear Models 219 3.1 Linear Models Sebastian waves good-bye to his brother, who is talking to a group of his friends approximately feet away. Sebastian then begins to walk away from his brother

More information

CH 59 SQUARE ROOTS. Every positive number has two square roots. Ch 59 Square Roots. Introduction

CH 59 SQUARE ROOTS. Every positive number has two square roots. Ch 59 Square Roots. Introduction 59 CH 59 SQUARE ROOTS Introduction W e saw square roots when we studied the Pythagorean Theorem. They may have been hidden, but when the end of a right-triangle problem resulted in an equation like c =

More information

COLLEGE ALGEBRA. Solving Equations and Inequalities. Paul Dawkins

COLLEGE ALGEBRA. Solving Equations and Inequalities. Paul Dawkins COLLEGE ALGEBRA Solving Equations and Inequalities Paul Dawkins Table of Contents Preface... ii Solving Equations and Inequalities... 3 Introduction... 3 s and Sets... 4 Linear Equations... 8 Application

More information

Special Theory of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay. Lecture - 15 Momentum Energy Four Vector

Special Theory of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay. Lecture - 15 Momentum Energy Four Vector Special Theory of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Lecture - 15 Momentum Energy Four Vector We had started discussing the concept of four vectors.

More information

Essential Statistics. Gould Ryan Wong

Essential Statistics. Gould Ryan Wong Global Global Essential Statistics Eploring the World through Data For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects

More information

Lesson 39. The Vine and the Branches. John 15:1-8

Lesson 39. The Vine and the Branches. John 15:1-8 L i f e o f C h r i s t from the gospel of J o h n Lesson 39 The Vine and the Branches John 15:1-8 Mission Arlington Mission Metroplex Curriculum 2010 Created for use with young, unchurched learners Adaptable

More information

Welcome back to Physics 211

Welcome back to Physics 211 Welcome back to Physics 211 The room is very full please move toward the center and help others find a seat. Be patient. The registration database is only updated twice per week. Get to know the people

More information

INTRODUCTION TO ANALYSIS OF VARIANCE

INTRODUCTION TO ANALYSIS OF VARIANCE CHAPTER 22 INTRODUCTION TO ANALYSIS OF VARIANCE Chapter 18 on inferences about population means illustrated two hypothesis testing situations: for one population mean and for the difference between two

More information

ESTIMATING STATISTICAL CHARACTERISTICS UNDER INTERVAL UNCERTAINTY AND CONSTRAINTS: MEAN, VARIANCE, COVARIANCE, AND CORRELATION ALI JALAL-KAMALI

ESTIMATING STATISTICAL CHARACTERISTICS UNDER INTERVAL UNCERTAINTY AND CONSTRAINTS: MEAN, VARIANCE, COVARIANCE, AND CORRELATION ALI JALAL-KAMALI ESTIMATING STATISTICAL CHARACTERISTICS UNDER INTERVAL UNCERTAINTY AND CONSTRAINTS: MEAN, VARIANCE, COVARIANCE, AND CORRELATION ALI JALAL-KAMALI Department of Computer Science APPROVED: Vladik Kreinovich,

More information

Data Mining Prof. Pabitra Mitra Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur

Data Mining Prof. Pabitra Mitra Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Data Mining Prof. Pabitra Mitra Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur Lecture 21 K - Nearest Neighbor V In this lecture we discuss; how do we evaluate the

More information

Objective: Recognize halves within a circular clock face and tell time to the half hour.

Objective: Recognize halves within a circular clock face and tell time to the half hour. Lesson 13 1 5 Lesson 13 Objective: Recognize halves within a circular clock face and tell time to the half Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief

More information

Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 33 The Diffie-Hellman Problem

More information

After completing the Orientation Overview exercises, you now know what this course is going to be about. You know what the course is going to cover.

After completing the Orientation Overview exercises, you now know what this course is going to be about. You know what the course is going to cover. After completing the Orientation Overview exercises, you now know what this course is going to be about. You know what the course is going to cover. Physical 1 is a fundamental introductory overview course

More information

Math 7 Notes Unit Two: Integers

Math 7 Notes Unit Two: Integers Math 7 Notes Unit Two: Integers Syllabus Objective: 2.1 The student will solve problems using operations on positive and negative numbers, including rationals. Integers the set of whole numbers and their

More information

Implicit Differentiation Applying Implicit Differentiation Applying Implicit Differentiation Page [1 of 5]

Implicit Differentiation Applying Implicit Differentiation Applying Implicit Differentiation Page [1 of 5] Page [1 of 5] The final frontier. This is it. This is our last chance to work together on doing some of these implicit differentiation questions. So, really this is the opportunity to really try these

More information

MITOCW ocw f99-lec30_300k

MITOCW ocw f99-lec30_300k MITOCW ocw-18.06-f99-lec30_300k OK, this is the lecture on linear transformations. Actually, linear algebra courses used to begin with this lecture, so you could say I'm beginning this course again by

More information

Sampling Distribution Models. Chapter 17

Sampling Distribution Models. Chapter 17 Sampling Distribution Models Chapter 17 Objectives: 1. Sampling Distribution Model 2. Sampling Variability (sampling error) 3. Sampling Distribution Model for a Proportion 4. Central Limit Theorem 5. Sampling

More information

June If you want, you may scan your assignment and convert it to a.pdf file and it to me.

June If you want, you may scan your assignment and convert it to a.pdf file and  it to me. Summer Assignment Pre-Calculus Honors June 2016 Dear Student: This assignment is a mandatory part of the Pre-Calculus Honors course. Students who do not complete the assignment will be placed in the regular

More information