The Cox-Ross-Rubinstein binomial pricing model, which retains the economic insights of the Black-Scholes-Merton version without requiring the use of advanced mathematical tools, is suitable for coverage in finance courses when the topic of options is covered. If the number of time steps in the Cox-Ross-Rubinstein model between the valuation date and the expiry date of an option approaches infinity, the two models will converge on statistical grounds. This pedagogic note addresses some computational issues as the number of time steps increases to high levels. It also provides a measure to counteract potential deterioration of computational precision. The spreadsheet-based illustration in this note complements very well the statistical justification for the convergence of the two models.
Machine learning (ML) education for non-programming students faces significant barriers when traditional approaches rely heavily on coding skills. This paper presents a novel spreadsheet-based curriculum that implements complete ML training algorithms without programming requirements. We introduce the "overwrite method" to enable interactive parameter updates in spreadsheet environments, addressing the fundamental challenge of iterative optimization while maintaining educational transparency. Our graduated implementation strategy provides complete training visualization for foundational models (linear regression, logistic regression, neural networks) and focuses on architectural understanding for complex models (CNNs, Transformers). The curriculum was evaluated through a quasi-experimental study with 48 engineering students from diverse students. Results demonstrate statistically significant learning improvements across all four learning objectives: model architecture understanding (r = 0.67), learning principles (r = 0.57), hyperparameter tuning skills (r = 0.32), and application judgement skills (r = 0.29). The spreadsheet-based approach successfully enables students to observe gradient descent dynamics, parameter convergence, and decision boundary evolution in real-time, providing intuitive understanding of ML concepts typically obscured in black-box implementations. This research establishes a new paradigm for accessible ML education that bridges theoretical knowledge with hands-on implementation experience.
The Cox-Ross-Rubinstein binomial option pricing model, which retains the economic insights of the Black-Scholes-Merton version without requiring advanced mathematical tools, is suitable for coverage in finance courses where the topic of options is covered. If the number of time steps in the Cox-Ross-Rubinstein model between the valuation date and the expiry date of an option approaches infinity, the two will converge on statistical grounds. This pedagogic note addresses some computational issues as the number of time steps increases to high levels. It also provides a measure to counteract the potential deterioration of computational precision. The spreadsheet-based illustration in this note complements very well the statistical justification for the convergence of the two models.
This pedagogic note considers the sum of reciprocals of polynomial numbers. Closed form expressions of the sum are currently available for twelve specific cases, from triangles to 26-sided polygons. Several of these expressions are from featured solutions to posted questions in college mathematics journals. A general expression of the sum, which is in terms of the digamma function and the Euler-Mascheroni constant, is also available for polygons with five sides or more. This note uses an Excel spreadsheet to assess numerically the adequacy of some partial sums and the equivalence of the two analytical approaches. The general expression will be useful for verifying any new additions to the current list of closed form expressions of the sum of the reciprocals of polynomial numbers.
The insight into physical phenomena can be understood better using graphs, which show their unique behavior. Two of these are oscillations (damped and driven) and radioactivity (decay and equilibrium). Manually plotting their graphs could be cumbersome work, and users or learners do not have the freedom to change a parameter and see the behavior for many conditions due to time consumption. This study integrates theoretical equations formulated for a classical oscillator and radioactive decay with simulations to have a better understanding of the physics concepts and the effects of varying several parameters. Spreadsheets, being the most basic software, are proved to be very useful as a simulation tool that facilitates learning beyond theoretical discourse. The aim is to offer a more effective and efficient teaching-learning process for STEM courses.
The purpose of this paper is to give an example of guided problem solving and using a spreadsheet to help solve a related series of mathematical problems. The context is that of side totals, where the numbers 1 - 2n are arranged three on each side of an n-sided polygon. The context allows for the problem to start small and easily accessible by exploring ways to arrange the numbers 1 - 6 on the sides of a triangle. From that beginning and with support from spreadsheet calculations, the investigation extends to finding arrangements of numbers that form equal side totals on squares and pentagons. From there, a number of patterns emerge that can be applied to polygons with many more sides and students can be guided to engage with the explorations by following patterns that arise in a simple context and applying those patterns to more complext contexts. Discovering the various patterns provides opportunities for students to have the Aha experience that accompanies the discovery of numerical patterns and problem solutions in mathematics. This article is designed to foster that experience amongst secondary students to whom the mathematical content of the problems will be readily accessible.
The surprising empirical finding in the finance literature that the 1/N investment strategy outperforms portfolio optimization, followed by some intense debate on the topic, has given credence to this simple approach in the investment world . This paper, which draws on an Excel-based assignment in an introductory finance course, examines equally-weighted portfolios closely. The examination reveals the hidden role of the correlation of returns in such portfolios. In the context of equity investments, this paper presents a simple way to estimate portfolio risk for the purpose of examining how it varies as stocks are added to an equally-weighted portfolio. The simple appproach introduced here also allows the aggregate contribution of the individual covariances of stock returns to be established. Further, it allows an alternative measure of portfolio risk, the Gini coefficient, to be used as well.
X-ray diffractometry is one of the most useful nondestructive techniques used to characterize crystalline substances. One can gain knowledge of structures and structure parameters, phases and texture, average grain size, crystalline stain and defects, from an XRD pattern. In this study, we develop a macro-enabled Microsoft Excel spreadsheet to study x-ray diffraction patterns. Through this spreadsheet x-ray diffraction patterns of different materials are analyzed to find the Miller indices and the lattice parameters. One must provide only the twenty values for all the peaks, and then a single click on the calculate button will immediately give the 'hkl' values for all the peaks. This spreadsheet can be used to index XRD patterns of cubical and hexagonal structures.
The objective of this article is to showcase the capabilities of the Microsoft Excel package in simulating the performance of the Rankine Cycle with a single bleed point. Thermodynamic properties are derived using specialized Excel tools designed for thermodynamics, with Microsoft Excel serving as the platform for these tools. The obtained properties undergo thorough testing to ensure accuracy, and the results demonstrate strong agreement with those found in other existing literature. Energy balance calculations on each component of the Rankine Cycle are conducted to determine the thermodynamic properties at different points. The extraction pressure and the respective mass fraction is being evaluated and analysed to understand the behaviour of the cycle.
Thermodynamics is an essential topic in Engineering education. Difficulties in teaching and learning thermodynamics are well known, and many efforts have been developed to improve the teaching of thermodynamic subjects. The solution of problems is the main task in Engineering education, and much effort must be carried out to describe strategies and standard procedures. Methodologies involving problem-based learning, group work, and e-learning appear very often as the best option to properly develop skills related to thermodynamics. The objective of the present work is to describe a project involving a combined methodology of problem-based learning and e-learning in Applied Thermodynamics in the Chemical Engineering program at the Universidad Rey Juan Carlos (Mosoles, Madrid, Spain). Students solved proposed problems using Excel worksheets in a short time; the activity was carried out voluntarily, individually, and without the professor's help. Grades obtianed in these activities were compared to grades from the standard evalaution methods used in the subject (exams and seminar problems). A stronger correlation was found between PBL/e-learning and exam grades than between seminars and exam grades, suggesting working group activities are of limited value. The opinion of the participating students also favoured the PBL/e-learning approach.
A spreadsheet is developed for modeling wind distribution through the Weibull distribution. Two parametes of the Weibull distribution are sufficient for the modeling. The Excel macro has been used to determine these parameters. The parameters are determined by six methods: graphical method (GM), maximum likelihood method (MLM), method of moments (MM), energy pattern factor model (EPFM), empirical method (EM), and modified maximum likelihood method (MMLM). Each of these six methods has a corresponding button on the spreadsheet; this button calculates parameters "k" and "c" of the Weibull distribution on activation. These buttons also find the average wind speed and statistical errors; root mean square errors (RMSE); chi-square statistics, and the coefficient of determination for validation of the results. To check the effectiveness of the spreadsheet, the wind speed data of Volkel, Gilze-Rijen, Eindhoven, and Herwijnen, cities in the Netherlands, during the years 2015 and 2016, were used. The data were obtained from the Royal Netherlnds Meterological Institute. The spreadsheets also generates the probability density function using parameter values obtained by the six methods; these are shown on a single plot of the probabilities against the wind speed.
During the covid pandemic we moved to a mixture of online, hybrid and in person teaching. In doing so we faced problems in teaching various modules in analytical geometry and calculus online. A graphical user interface (GUI) teaching tool was therefore developed to teach several analytical geometry modules to college and undergraduate university students. These executable spreadsheets can help physics and mathematics students practice numerous principles of analytical geometry with few inputs and comprehensive solutions with a single click. Because spreadsheets are so widespread, they can be used to calculate equations of straight lines, planes, areas, and volumes in 3-directional geometry. Some online vector GUIs display the outcomes; however, this GUI illustrates the computation methods to get the results, making it easier to study the topic. The designed GUI also aids mentors in their lab work and tests by creaing various papers with answer keys.
Spreadsheets are ubiquitous and easily understandable. They are used for calculations in scientific quantitative analysis and graphing. Scientists have used spreadsheets for calculations, simulations, and graphical user interface (GUI) applications. In the current work, we develop a spreadsheet that can be used to calculate three types of solar radiation: direct beam solar radiation, (BSR), diffused solar radiation (DSR), and global solar radiation (GSR) for any region in the world. The necessary input data for the calculations are latitude, longitude, and prime meridian. The GUI calculates BSR, DSR, and GSR for a particular day of the month; i.e. the daily solar radiation, and for a specific time of the year; i.e. the year solar radiation. The GUI also compares three types of radiation in three cities. The spreadsheet can teach students about solar radiation and its dependence on geographical location. The student can use this GUI easily. This graphing utility differs from other online tools because it takes fewer inputs and provides accurate results.
Non-linear regression is used to fit data to a broad range of functions. In non-linear regression, a non-linear model is used to explain the relationship between the dependent variable and one or more independent variables. This paper demonstrates the use of the Gauss-Newton method in Microsoft Excel to perform non-linear regressions.
Spreadsheet modeling courses often introduce students enrolled in undergraduate and master's degree programs in decision sciences and data analytics to key concepts in optimization and simulation. Use of Visual Basic for applications (VBA) can significantly extend Excel's capabilities. For instance, with VBA one can create one's own functions, automate repetitive tasks, perform a series of interrelated activities (e.g., setting up and running a model with no user intervention). provide a front-end interface for a model, and tackle complex problems that do not have ready-made textbook solutions. This article provides several relevant examples for students taking a spreadsheet modeling course that can introduce them in a few hours to some of the possibilities that VBA opens for enhancing model versatility and usability.
Spreadsheets are often used in mathematics courses to support various learning objectives. The present paper analyzes different ways in which a spreadsheet can be used to calculate sample standard deviation, a frequency table and histogram, future value of a series of deposits, and a periodic loan payment. The mathematical and spreadsheet knowledge that students need to solve a problem using each of these techniques is considered as well as the levels of the revised Bloom's Taxonomy involved in each task. The suitability of each method for different groups of students is also addressed.
A 1981 mathematical article by Kenneth S. Miller has considered the inverse of the sum of matrices. The ingenuity of the Miller approach is that it has reached an expression without the entanglement of the inverse of the sum of some other matrices. The first part of the Miller approach, as provided in a lemma, has established analytically the inverse of the sum of a full-rank matrix and a rank-1 matrix. By substituting the rank-1 matrix with a more general matrix and expressing the latter matrix as the sum of some rank-1 matrices, the second part, which is Miller’s theorem, has used the lemma recursively to reach the end result. This note provides a pedagogic rendition of the Miller proof, along with a spreadsheet-based illustration.
This paper describes a novel approach for exploring counting and pattern recognition in early elementary classrooms that ties numerical patterns to geometric patterns. Active-learning exercises that start out face-to-face (or using the virtual Class Circle sheet of the Polygons and Stars Excel file) can be explored quickly and more fully using the Polygons and Stars sheets. This file can be used by the teacher in the classroom, as well as by students undertaking independent explorations. Such explorations help energize young learners; as they explore, extract, and explain what they have found, they begin to recognize the beauty inherent in mathematical patterns.
Sylvester’s criterion, which verifies the positive definiteness of any real symmetric matrix by examining the signs of all leading principal minors, is an excellent analytical tool. However, as noted by several authors in various academic fields, misapplications of the tool include its unjustified use for non-symmetric matrices and its unjustified extension for verifying the positive semidefiniteness of matrices. As remedies are available, this paper provides a pedagogic illustration that connects the corresponding tests for the positive definiteness and the positive semidefiniteness of a matrix to the underlying concepts. Drawing on standard materials in linear algebra, this paper uses self-contained Excel worksheets to illustrate the concepts involved and to generate matrices that are suitable for use in courses covering Sylvester’s criterion. This paper also suggests the use of some Excel-based exercises for students, as an alternative approach to cover the same topic.
This “in the classroom” note stems from using a spreadsheet in exploring an open problem in mathematics by pre-college students of different grade levels. While being accessible to the upper elementary and middle school students, the activities the note suggests reveal the tool’s potential for some deeper investigations towards fostering the students’ interest in more advanced mathematics. Due to a simple access to the problem combined with its rich spreadsheet-enhanced milieu for questioning and conjecturing, many collateral problems can be posed by teachers and their students alike. A possibility of extending and deepening one’s experience in mathematical observation and computational verification which goes beyond an average mathematics classroom and aimed at “special needs” of mathematically advanced students is discussed.
