Using Microsoft Excel to Bring Basic Math, Science, Statistics, Business and Finance Application Principles Alive for Your Students Gurmukh Singh, Ph.D

Using Microsoft Excel to Bring Basic Math, Using Microsoft Excel to Bring Basic Math, Science, Statistics, Business and Finance Science, Statistics, Business and Finance

Application Principles Alive for Your Students Application Principles Alive for Your Students

Gurmukh Singh, Ph.D. Gurmukh Singh, Ph.D.

Department of Computer and Information SciencesDepartment of Computer and Information Sciences

State University of New York at FredoniaState University of New York at Fredonia

Fredonia, NY 14063Fredonia, NY 14063

[email protected]@fredonia.edu

Gannon University’s Second Annual Regional Symposium Gannon University’s Second Annual Regional Symposium Excellence and Innovation in Teaching and Learning Excellence and Innovation in Teaching and Learning

May 23, 2008 May 23, 2008

11Presentation by G. Singh at Gannon Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008University, Erie, PA, May 23, 2008

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Why Microsoft Excel 2007/2003 in College?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 Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008University, Erie, PA, May 23, 2008

Presentation by G. Singh at Gannon Presentation by G. Singh at Gannon University, Erie, PA, May 23, 2008University, Erie, PA, May 23, 2008 33

Why Microsoft Excel 2007/2003 in College?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]

Main Objectives of my PresentationMain Objectives of my Presentation

• Use of Microsoft Software Excel 2007/2003 Software Use of Microsoft Software Excel 2007/2003 Software [1,5] for teaching college and university level curriculum [1,5] for teaching college and university level curriculum in natural science, medical science, business and in natural science, medical science, business and engineering applications for college undergraduatesengineering applications for college undergraduates

1. Simple algebra and trig calculations 2. Business and finance computations for College students3. Individual Retirement Accounts (IRAs) for employees 4. Math and statistics majors5. Bio-medical science students6. Creating Professor’s grade-book for instructors7. Computational physics and physics education 8. Computer science majors


Development of Interactive Applications with Development of Interactive Applications with Excel 2007/2003Excel 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


Development of Interactive Applications with Development of Interactive Applications with Excel 2003/2007 (contd.)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


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Fig. 1(a): Fig. 1(a): Typical Excel 2007 Interface, Home Tab Typical Excel 2007 Interface, Home Tab


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Fig. 1(b): Fig. 1(b): Typical Excel 2003 Interface, Main MenuTypical Excel 2003 Interface, Main Menu


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Excel 2007/2003 Functions being used in Excel 2007/2003 Functions being used in Interactive ApplicationsInteractive 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])

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Fig. 2: Fig. 2: Elementary Multiplication TablesElementary Multiplication Tables


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Fig. 3: Fig. 3: Elementary Division TablesElementary Division Tables


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Fig. 4: Fig. 4: Basic Interactive Trig TablesBasic Interactive Trig Tables


Basic Interactive Trig Tables in Mathematics for High School Teachers Angle, θ sin θ cos θ tan θ sec θ cosec θ cot θ Initial 60.00

60.00 0.8660 0.5000 1.7321 1.1547 2.00000 0.5773 61.00 0.8746 0.4848 1.8041 1.1434 2.06267 0.5543 62.00 0.8829 0.4695 1.8807 1.1326 2.13005 0.5317 63.00 0.8910 0.4540 1.9626 1.1223 2.20269 0.5095 64.00 0.8988 0.4384 2.0503 1.1126 2.28117 0.4877 65.00 0.9063 0.4226 2.1445 1.1034 2.36620 0.4663 66.00 0.9135 0.4067 2.2460 1.0946 2.45859 0.4452 67.00 0.9205 0.3907 2.3559 1.0864 2.55930 0.4245 68.00 0.9272 0.3746 2.4751 1.0785 2.66947 0.4040 69.00 0.9336 0.3584 2.6051 1.0711 2.79043 0.3839 70.00 0.9397 0.3420 2.7475 1.0642 2.92380 0.3640 71.00 0.9455 0.3256 2.9042 1.0576 3.07155 0.3443 72.00 0.9511 0.3090 3.0777 1.0515 3.23607 0.3249 73.00 0.9563 0.2924 3.2709 1.0457 3.42030 0.3057 74.00 0.9613 0.2756 3.4874 1.0403 3.62796 0.2867 75.00 0.9659 0.2588 3.7321 1.0353 3.86370 0.2679 76.00 0.9703 0.2419 4.0108 1.0306 4.13357 0.2493 77.00 0.9744 0.2250 4.3315 1.0263 4.44541 0.2309 78.00 0.9781 0.2079 4.7047 1.0223 4.80973 0.2126 79.00 0.9816 0.1908 5.1446 1.0187 5.24084 0.1944 80.00 0.9848 0.1736 5.6713 1.0154 5.75877 0.1763 81.00 0.9877 0.1564 6.3138 1.0125 6.39245 0.1584 82.00 0.9903 0.1392 7.1155 1.0098 7.18530 0.1405 83.00 0.9925 0.1219 8.1445 1.0075 8.20551 0.1228 84.00 0.9945 0.1045 9.5145 1.0055 9.56677 0.1051 85.00 0.9962 0.0872 11.4303 1.0038 11.47371 0.0875 86.00 0.9976 0.0698 14.3010 1.0024 14.33559 0.0699 87.00 0.9986 0.0523 19.0818 1.0014 19.10732 0.0524 88.00 0.9994 0.0349 28.6377 1.0006 28.65370 0.0349

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Fig. 5: Fig. 5: Business and Finance ApplicationsBusiness and Finance Applications


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Fig. 6: Fig. 6: Monthly Home Mortgage Payment Monthly Home Mortgage Payment ApplicationApplication


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Fig. 7: Fig. 7: Individual Retirement Account (IRA) Individual Retirement Account (IRA) ApplicationApplication


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Fig. 8: Fig. 8: Statistical Analysis ApplicationStatistical Analysis Application


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Fig. 9:Fig. 9: Simulations of Recessive Gene Simulations of Recessive Gene Contribution in Population Growth ApplicationContribution in Population Growth Application


Female Gene

Male Gene Baby Recessive Recessive Genes

dominant dominant dominant 0 Generation Trials Babies Ratio

recessive recessive recessive 1 1.0 15 4 2

recessive dominant dominant 0 2.0 30 9 2

dominant recessive dominant 0 3.0 62 17 2








recessive recessive recessive 1 11.0 16000 4089

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Fig. 10: Fig. 10: Population growth with generationsPopulation growth with generations


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Fig. 11: Fig. 11: Dr. Singh’s Virtual Grade-bookDr. Singh’s Virtual Grade-book


• 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

Some Examples of Projectile Motion in Physics


Theory and Algorithm of Projectile MotionTheory and Algorithm of Projectile Motion

dt

dxxv .

dt

dyyv

,dt

dvxa

x

dt

dvya

y

,),,( xx matvxF x yy matvyF y ),,(

,22

100

txatx

vxx 22

100

tyaty

vyy

,0

txaxvxv tyay

vyv 0


Theory and Algorithm of Projectile MotionTheory and Algorithm of Projectile Motion

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.


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.

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.

Interactive Simulation of Projectile Motion


Fig. 12: Partial Results of Interactive Simulation

Serial # Time (sec) Velocity (m/s) Calculated Height (m) Exact Height (m) % Error in Height (m)1 0.0000 0.0000 100.0000 99.5406 -0.45942 0.0125 -0.1225 99.9985 99.9992 0.00083 0.0250 -0.2450 99.9954 99.9969 0.00154 0.0375 -0.3675 99.9908 99.9931 0.00235 0.0500 -0.4900 99.9847 99.9878 0.00316 0.0625 -0.6125 99.9770 99.9809 0.00387 0.0750 -0.7350 99.9678 99.9724 0.00468 0.0875 -0.8575 99.9571 99.9625 0.00549 0.1000 -0.9800 99.9449 99.9510 0.0061

10 0.1125 -1.1025 99.9311 99.9380 0.006911 0.1250 -1.2250 99.9158 99.9234 0.007712 0.1375 -1.3475 99.8989 99.9074 0.008413 0.1500 -1.4700 99.8806 99.8898 0.009214 0.1625 -1.5925 99.8607 99.8706 0.010015 0.1750 -1.7150 99.8392 99.8499 0.010716 0.1875 -1.8375 99.8163 99.8277 0.011517 0.2000 -1.9600 99.7918 99.8040 0.012318 0.2125 -2.0825 99.7657 99.7787 0.013019 0.2250 -2.2050 99.7382 99.7519 0.013820 0.2375 -2.3275 99.7091 99.7236 0.014621 0.2500 -2.4500 99.6784 99.6938 0.015422 0.2625 -2.5725 99.6463 99.6624 0.016123 0.2750 -2.6950 99.6126 99.6294 0.016924 0.2875 -2.8175 99.5774 99.5950 0.017725 0.3000 -2.9400 99.5406 99.5590 0.0185


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.

Horizontal Range of Projectile MotionHorizontal Range of Projectile Motion


Fig. 13:Fig. 13: A plot of projectile height, A plot of projectile height, HH versus time, versus time, tt


Fig. 14: Fig. 14: Two slide bars to change initial Two slide bars to change initial boundary conditions boundary conditions

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.


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.

Interactive Simulations of Nine Rolling DiceInteractive 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.


Fig. 15:Fig. 15: Simulated value of number of dots on the Simulated value of number of dots on the six faces of each dice in rolling of nine dicesix faces of each dice in rolling of nine dice

Dice 1 Dice 2 Dice 3 Dice 4 Dice 5 Dice 6 Dice 7 Dice 8 Dice 9 Total Total/Max3 4 1 3 5 3 3 6 3 31 0.704 6 3 6 2 3 3 3 1 31 0.703 4 2 5 4 4 4 6 2 34 0.776 5 1 1 1 3 5 3 1 26 0.595 1 3 6 1 6 5 1 3 31 0.704 1 2 2 2 6 2 1 6 26 0.594 4 6 4 2 2 3 5 2 32 0.733 6 1 6 6 1 2 3 5 33 0.752 1 3 4 5 5 4 6 4 34 0.772 6 1 4 4 3 4 4 2 30 0.682 6 1 1 5 6 5 6 5 37 0.846 1 6 6 5 1 6 4 6 41 0.934 1 6 5 5 4 2 4 3 34 0.773 6 5 5 4 3 3 5 6 40 0.916 5 4 3 1 3 2 6 1 31 0.701 1 6 2 3 2 3 5 6 29 0.661 5 2 2 2 1 6 1 6 26 0.595 2 3 1 2 5 4 2 4 28 0.641 3 4 1 6 6 5 4 2 32 0.733 5 3 5 6 4 6 4 4 40 0.915 1 6 6 4 6 3 6 3 40 0.916 3 6 1 3 4 6 2 2 33 0.751 1 1 6 2 5 2 2 6 26 0.594 3 3 1 4 3 2 2 6 28 0.64


Fig. 16:Fig. 16: A plot of ratio of total score in one row to the A plot of ratio of total score in one row to the maximum score as a function of number of trialsmaximum score as a function of number of trials



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.


Concluding RemarksConcluding Remarks

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 (contd.)Concluding Remarks (contd.)

• 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


AcknowledgementsAcknowledgements


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.

ReferencesReferences

1. 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.

2. Introduction to Interdisciplinary Computational Science Education for Educators, SC07 Education Program Summer Workshop Series, Buffalo State College, June 3-9, 2007.

3. http://www.sun.com/; http://www.ibm.com/; http://www.research.att.com/.4. 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).

5. R. Grauer and M. Barber, Microsoft Office Excel 2003 (Comprehensive Revised Ed), Prentice Hall, Inc. (2006); R. Grauer and J. Scheeren, Microsoft Office, Excel 2007 (Comprehensive Ed), Prentice Hall Inc. (2008).

6. G. Mendel, "Experiments on Plant Hybrids." In: The Origin of Genetics: A Mendel Source Book, (1866).

7. 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)


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Using Microsoft Excel to Bring Basic Math, Science, Statistics, Business and Finance Application Principles Alive for Your Students Gurmukh Singh, Ph.D