Gurmukh Singh, Ph.D. Department of Computer and Information Sciences

1. Using Microsoft Excel to Bring Basic Math, Science, Statistics, Business and Finance Application Principles Alive for Your Students Gurmukh Singh, Ph.D. Department of Computer and Information Sciences State University of New York at Fredonia Fredonia, NY 14063 singh@fredonia.edu Gannon University’s Second Annual Regional Symposium Excellence and Innovation in Teaching and Learning May 23, 2008 Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

2. Why Microsoft Excel 2007/2003 in College? • Development and advancement in high speed micro-computers such as IBM and Mac based PCs [1,3] • Portable laptops as versatile class-room tools to teach undergraduate science and engineering curriculum [2] • Microcomputer machines employ several software systems such as Excel, Access, Word, PowerPoint, Groove, InfoPath, OneNote, Outlook, Publisher, FrontPage etc [1]. • Object oriented computing languages like C++, C#, Visual Basic (VB), Java Script, SQL etc. [3] • Among these software systems, Microsoft Excel is the second most used software system for undergraduate, graduate teaching in colleges, scientific labs, private companies, businesses and banks in our country [1,3,5] Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

3. Why Microsoft Excel 2007/2003 in College? • Adoption of internet technologies in undergraduate science and engineering curriculum • International/National conferences to enhance and share the knowledge gained with other educators and researchers [2, 4] • Use of Internet technologies to interactively teach in undergraduate and graduate classroom setting or during distant learning in virtual universities, which is a very effective teaching tool for the science and engineering curricula [2] Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

4. Main Objectives of my Presentation Use of Microsoft Software Excel 2007/2003 Software [1,5] for teaching college and university level curriculum in natural science, medical science, business and engineering applications for college undergraduates Simple algebra and trig calculations Business and finance computations for College students Individual Retirement Accounts (IRAs) for employees Math and statistics majors Bio-medical science students Creating Professor’s grade-book for instructors Computational physics and physics education Computer science majors Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

5. Development of Interactive Applications with Excel 2007/2003 • Simple multiplication and division tables for elementary math education students • Creation of trig tables for high school students/teachers • Car and mortgage payment calculations for business and finance majors plus IRA accounts for employees working throughout America • Statistical analysis of virtual data of four sections in SUNY Fredonia by Dr. Singh • Model Mendel’s Laws of heredity [6,7] for recessive genes for biological instructors/majors Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

6. Development of Interactive Applications with Excel 2003/2007 (contd.) • Create professor’s grade-book for College and University faculty, and also for future generation of teachers (college students) • Study the random process of rolling of two or more dice in a casino game for a statistical problem in computer science education • Some interesting and important interactive applications to perform simulations of projectile motion such as a missile launched from an airplane to hit a target on ground for physics education, computational physics and engineering majors Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

7. Fig. 1(a): Typical Excel 2007 Interface, Home Tab Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 7

8. Fig. 1(b): Typical Excel 2003 Interface, Main Menu Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 8

9. Excel 2007/2003 Functions being used in Interactive Applications • Payment function: PMT(rate, nper, pv, [fv], [type]) • Future Value function: FV(rate, nper, pmt, [pv]. [type]) • Sum function: SUM(A1:A20) • Average function: AVERAGE(A1:A20) • Maximum function: MAX(A1:A20) • Minimum function: MIN(A1:A20) • Median function: MEDIAN(A1:A20) • Standard Deviation function: STDEV(A1:A20) • Vertical Lookup function: • VLOOKUP(lookup_value, table_array, col_index_num, [range_lookup]) Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 9

10. Fig. 2: Elementary Multiplication Tables Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 10

11. Fig. 3: Elementary Division Tables Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 11

12. Fig. 4: Basic Interactive Trig Tables Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 12

13. Fig. 5: Business and Finance Applications Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 13

14. Fig. 6: Monthly Home Mortgage Payment Application Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 14

15. Fig. 7: Individual Retirement Account (IRA) Application Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 15

16. Fig. 8: Statistical Analysis Application Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 16

17. Fig. 9: Simulations of Recessive Gene Contribution in Population Growth Application Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 17

18. Fig. 10: Population growth with generations Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 18

19. Fig. 11: Dr. Singh’s Virtual Grade-book Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008 19

20. Some Examples of Projectile Motion in Physics • Launching of a cruise missile from an air plane to hit an enemy post • Motion of a space shuttle or a rocket from launching pad • Firing an artillery shell to destroy an enemy post • Firing of a cannon ball from a cannon • Hitting of a baseball with baseball bat • Hitting of a golf ball with golf club • Firing of a bullet from a gun or a pistol • Shooting of an arrow with a bow during hunting • Punting of a football during ball game • Kicking of a football during kick off in ball game • Study the projectile motion in a physics lab Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

21. Components of the projectile velocity v(x,y,t), acceleration a(x,y,t), force F(x,y,t), r(x,y,t) position vector in two-dimensional space are: • (1) • (2) • (3) • (4) • (5) Theory and Algorithm of Projectile Motion Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

22. where x0, y0 and v0x, v0y are initial position coordinates and initial components of velocity of projectile along x- and y-directions, respectively. Eq. (4) and Eq. (5) are called kinematic equations of projectile motion. We employed these equations to simulate the projectile trajectory under action of gravity with the simplest assumption of no air resistance and implemented boundary conditions for the present problem (i.e. ax = 0, ay = g = -9.80 m/s2, vy = V,v0y = V0,y = H, and y0 = H0), so that Eq. (4) and Eq. (5) could be written as follows along y-axis   V = Vo+gt,(6) H’ = Ho + Vot + 0.5gt2. (7) These equations will be used to simulate the projectile’s exact velocity V and exact height H’ at a given instant of time. Theory and Algorithm of Projectile Motion Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

23. Interactive Simulation of Projectile Motion Eq. (6) and Eq. (7) are used to simulate projectile motion using Microsoft Excel 2007 [5]. A cell formula in Excel always starts with an equals sign (=), and thus their corresponding cell formulas for simulation of exact velocity and exact height should be typed in Excel spreadsheet as V = Vo+ g*A2 (8) H’ = Ho + Vo*A2 + 0.5*g*A2^2 (9) where Vo = 0 m/s and Ho = 100 m is the value of initial velocity and height of the projectile in y-direction, and A2 = dt = 0.0125 s represents the relative cell reference for a change in time interval, dt, which is memorized in Excel by some thing called “Defined Name” [1,5] and its value may exist in a different cell, whose cell reference could be used in Eq. (8) and Eq. (9) for the present simulation work. Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

24. Interactive Simulation of Projectile Motion We are depicting only the first forty simulated values of exact velocity, V and exact height, H’, of the projectile in Table of Fig. 11. Also given in this Table is the computed height of the projectile and % error in height. Computed height H is always a little less than that of the exact height H’. For 93% of the simulated data points, the magnitude of percent error between simulated height and actual height is < 4.0%, which indicates that the accuracy in computed values of projectile height is pretty good, which further proves that the chosen time interval dt = 0.0125 s almost satisfies the necessary and sufficient condition of differential calculus that in the limit of infinitesimal time interval, Δt → 0 for the projectile motion. Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

25. Fig. 12:Partial Results of Interactive Simulation Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

26. Horizontal Range of Projectile Motion For 93% of the simulated values, magnitude of percent error between computed height and actual height is < 4.0%, which indicates that the accuracy in computed values of projectile height is pretty good. The magnitude of horizontal range, R, of projectile during its time of flight t = 4.775, assuming a constant speed of airplane, Vairplane = 500 miles/hour along x-axis, can be obtained from kinematic equation Eq. (4) by using the initial boundary conditions, i.e., x = R, ax = 0, x0 = 0 and v0x = Vairplane: R = tVairplane = 1067 m (10) R is the distance where the projectile will hit a target on the ground. In the present problem, R = 1.07 km, which can be increased either by increasing airplane’s speed with respect to ground or by imparting some initial thrust to the projectile at launch time or by a combination of both. Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

27. Fig. 13:A plot of projectile height, H versus time, t Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

28. Fig. 14: Two slide bars to change initial boundary conditions 1 2 Two slider bars are used to perform simulations with different initial velocity V0 of the projectile and at a different initial height H0 of the airplane. Slide bar 1 represents the instantaneous initial height of the projectile, whereas slide bar 2 shows the initial velocity of the projectile at launch time. The initial height, H0 and initial velocity, V0 of the projectile can be increased or decreased by clicking on right or left hand side arrow existing on each end of a slide bar. Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

29. Interactive Simulations of Nine Rolling Dice To simulate the rolling process of nine dice in a casino game, once again, we employ the latest version of Microsoft Excel 2007/2003 software. To do the simulations, we use a built-in pseudo number generating function called RAND( ), which can generate all kinds of fractional numbers between 0 and 1. As none of the faces of each dice has marked with zero a dot, one is should include this fact while generating the random numbers with the generating function RAND(). Cell formula to create non-zero random numbers for the rolling of nine dice should also include a factor of 6, which is multiplied with the pseudo number generating function RAND( ) to take into account the fact of six faces of each dice, and a factor of unity is added to it to get rid of zero value generated random numbers. The random numbers thus generated for nine rolling dice are given in Table of Fig. 15 in its first nine columns. Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

30. Interactive Simulations of Nine Rolling Dice The random numbers thus generated for nine rolling dice are given in Table of Fig. 15 in its first nine columns. Column ten shows the sum total of scores obtained for all the nine dice in one trial. Eleventh column represents the ratio of sum total score of all nine dice in one row to the maximum score among all 200 data values in column ten of Table in Fig. 15. If one double clicks any cell of generated data, and then hits the ENTER key on the keyboard, all simulated random numbers for nine dice will change instantaneously and consequently, the total score in a single row normalized with the maximum score of the tenth column data values will also change. Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

31. Fig. 15:Simulated value of number of dots on the six faces of each dice in rolling of nine dice Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

32. Fig. 16: A plot of ratio of total score in one row to the maximum score as a function of number of trials Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

33. Interactive Simulations of Nine Rolling Dice In Fig. 16, we display a graph of this normalized total score as a function of number of trials. This graph has several peaks and valleys and it looks like the replica of an Electrocardiograph (ECG), which is obtained for a patient with some defect in the heart causing an irregular heart-beat. The interactive plot of Fig. 16 has in general, one or two peaks with a maximum value equals unity, and the remaining peaks always have values less than unity. The location of the maximum peak values and the nature of the plot changes with each new simulation, showing pretty interesting application of Excel 2007/2003 for computer science and medical undergraduates. Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

34. In conclusion, we may emphasize that the current interactive presentation employs Excel 2007/2003 [1, 5] software system, which has quite important implications in mathematics, business and finance, statistics, biological and medical sciences, computational physics and physics education, computer science as well as in engineering curriculum: • Math elementary school teachers can very efficiently show their students creation of multiplication and division tables • High school teachers can demonstrate the use of basic trig tables to their students • For business and finance majors, college/university instructors can use Excel software system to calculate monthly car payment, home mortgage payment and future value of an investment like individual retirement account (IRA) funds in 401K plans • In biological and medical sciences, it is possible to empirically formulate of Mendel’s Laws of heredity for the recessive/dominant genes of hybrid Pesium species [6,7] Concluding Remarks Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

35. In physics students will learn how to simulate the basic concept of projectile motion under the action of constant gravitational acceleration with no air resistance • In computer science, students could visualize the real time application of this fundamental concept of physics in a virtual laboratory. • Further, interactive application involving rolling of nine dice in a casino game gives a nice example of statistical and computer science problem in virtual lab • From the same interactive application, medical students can have an idea of irregular heart-beat of a patient suffering from heart attack or stroke, which has been proven with the help of a plot of normalized total score as a function of the number of trials from the simulations of nine rolling dice • Lastly creation and designing of Professor’s grade-book could be extremely useful and time saving application for college/university instructors and for future teachers Concluding Remarks (contd.) Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

36. I am thankful to Dr. Richard Reddy, Director, Office of Faculty Development, SUNY at Fredonia, for his useful comments and suggestions in writing the current proposal. Special thanks are also due to Dr. Virginia Horvath, Vice President Academic Affairs, SUNY at Fredonia for approving and funding my visit to attend the Second Annual Regional Symposium, Excellence and Innovation in Teaching and Learning, held at Gannon University, Erie, PA. I am also thankful to Dr. Khalid Siddiqui, Professor & Chairman, Department of Computer and Information Sciences, SUNY at Fredonia, to provide me the necessary computational facilities. Acknowledgements Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008

37. Microsoft Corporation, One Microsoft Way, Redmond, WA 98052-6399 and also visit the website http://www.microsoft.com/en/us/default.aspx for further information. Introduction to Interdisciplinary Computational Science Education for Educators, SC07 Education Program Summer Workshop Series, Buffalo State College, June 3-9, 2007. http://www.sun.com/; http://www.ibm.com/; http://www.research.att.com/. B. Boghosian, G. D. Doolen and D. P. Landau, International Conference on Computational Physics, CCP 99 held at Atlanta, GA on 20-26 March, 1999 and published in Comp. Phys. Comm. Vol. 127, 1-171 (2000); N. J. Giordano and H. Nakanishi, Computational Physics, (2nd Ed.), Prentice Hall Inc. (2006). R. Grauer and M. Barber, Microsoft Office Excel 2003 (ComprehensiveRevised Ed), Prentice Hall, Inc. (2006); R. Grauer and J. Scheeren, Microsoft Office, Excel 2007 (Comprehensive Ed), Prentice Hall Inc. (2008). G. Mendel, "Experiments on Plant Hybrids." In: The Origin of Genetics: A Mendel Source Book, (1866). C. Darwin, "On the Origin of Species by Means of Natural Selection, or the Preservation of Favored Races in the Struggle for Life," p. 162 (1859) References Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008