Mathematics Commons^™

12: Polar Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarPath.nb allows the user to input any polar function and use a slider to see how the path is created. That is, it will allow the user to see the order in which the petals or loops are created.

02: Poly Basics 1, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics1.nb deals with the graphs of polynomial functions of higher degrees. In this notebook, each factor is linear.

05: Limit Definition, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

LimitDefinition.nb asks the user to input a function. Then use the vertical slider to change the size of E. An appropriate value of 8 will be given.

14: Polar Vs Rectangular Animation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarVsRectangularAnimation.nb allows the user to input a polar function and then relates the graphs of r = ƒ(theta) and y = ƒ(x).

16: Sequences And Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.

15: Plotting S(N), Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PlottingS(n).nb animates the second section of the preceding notebook. After inputting the formula for a sequence, this animates both the sequence itself and the sequence of partial sums together as n increases.

12: Parametric Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.

16: Seeing Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SeeingSeries.nb allows the user to enter an explicit formula for the terms of a sequence. Then it animates the pattern of the sequence of partial sums. This is particularly helpful to understand conditional convergence with alternating series, but it may be used on series with all positive terms, whether convergent or divergent.

06: Reciprocal Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ReciprocalFunctions.nb asks the user to input a function. The notebook will graph the original function and its reciprocal.

06: Random Riemann, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RandomRiemann.nb takes a function, values for xmin and xmax, and a number n that represents the number of rectangles desired. This will create random subintervals with random points inside each subinterval, and then it will draw the corresponding Riemann sum. Values for the approximation and the actual value of the integral are given. This allows students to see how close (or distant) the approximation is and to visualize a wide variety of Riemann sums. Increasing values of n should help students understand the limiting process more clearly.

17: Maclaurin Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

MaclaurinSeries.nb gives animations for popular Maclaurin series. It shows the series with increasing values of n both graphically and analytically.

02: Derivative Approximation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DerivativeApproximation.nb contains two sections. Both allow the user to input a function and an x-window and to vary the center point. Then the value of h may be changed. The first section will show a symmetric approximation while the second shows a one-sided approximation.

Random Tropical Curves, Magda L. Hlavacek

HMC Senior Theses

In the setting of tropical mathematics, geometric objects are rich with inherent combinatorial structure. For example, each polynomial $p(x,y)$ in the tropical setting corresponds to a tropical curve; these tropical curves correspond to unbounded graphs embedded in $\R^2$. Each of these graphs is dual to a particular subdivision of its Newton polytope; we classify tropical curves by combinatorial type based on these corresponding subdivisions. In this thesis, we aim to gain an understanding of the likeliness of the combinatorial type of a randomly chosen tropical curve by using methods from polytope geometry. We focus on tropical curves corresponding to quadratics, …

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Classifying The Jacobian Groups Of Adinkras, Aaron R. Bagheri

HMC Senior Theses

Supersymmetry is a theoretical model of particle physics that posits a symmetry between bosons and fermions. Supersymmetry proposes the existence of particles that we have not yet observed and through them, offers a more unified view of the universe. In the same way Feynman Diagrams represent Feynman Integrals describing subatomic particle behaviour, supersymmetry algebras can be represented by graphs called adinkras. In addition to being motivated by physics, these graphs are highly structured and mathematically interesting. No one has looked at the Jacobians of these graphs before, so we attempt to characterize them in this thesis. We compute Jacobians through …

On The Graceful Cartesian Product Of Alpha-Trees, Christian Barrientos, Sarah Minion

Theory & Applications of Graphs

A graceful labeling of a graph G of size n is an injective assignment of integers from the set {0,1,…,n} to the vertices of G such that when each edge has assigned a weight, given by the absolute value of the difference of the labels of its end vertices, all the weights are distinct. A graceful labeling is called an α-labeling when the graph G is bipartite, with stable sets A and B, and the labels assigned to the vertices in A are smaller than the labels assigned to the vertices in B. In this …

Applications Of Laplace Transform, Andre Cocagne

Senior Honors Theses and Projects

Many students of the sciences who must have background in mathematics take courses up to, and including, differential equations. In this course, one of the topics covered is the Laplace transform. Coming to prominence in the late 20^th century after being popularized by a famous electrical engineer, knowledge on how to do the Laplace transform has become a necessity for many fields. While it is discussed and examples are given of how it is used, none of its applications are explored in depth in a class like differential equations. As such, this project seeks to showcase some of the …

Study Guide For Cuny Elementary Algebra Final Exam (Ceafe), Olen Dias, William Baker, Amrit Singh

Open Educational Resources

No abstract provided.

Studying “Moments” Of The Central Limit Theorem, Benjamin A. Stark

The Mathematics Enthusiast

The central limit theorem ranks high amongst the most important discoveries in the field of mathematics over the last three hundred years. This theorem provided a basis for approximation that turned the question of reaction into the art of prediction. This paper aims to map a course for the history and evolution of the famed theorem from its’ initial origins in 1733, from Abraham de Moivre’s inquiries to the most recent expressions of the theorem. The journey encompassing central limit theorem includes reformations of definition, relaxing of important associated conditions, and numerous types of rigorous proofs.

Critical Examination Of Ways Students Mirror The Teacher’S Classroom Practice: What Does It Mean To Be Successful At Mathematics?, Paula Guerra, Woong Lim

The Mathematics Enthusiast

In this paper, the authors report the mathematical learning experiences of “successful” female students in secondary mathematics classrooms taught by a “successful” teacher with the traditional mathematics’ behaviorist approach. The authors’ claim that the traditional view of mathematics held by the teacher and supported by the school system could not promote rigorous mathematics for girls to understand the importance of mathematical thinking as a foundation for success in mathematics-related professions. The authors recommend future studies creating opportunities for discussion in the field about the teacher’s view on mathematics, classroom practice, and how these resonate with girls’ experiences of learning mathematics.

Coherence And Enrichment Across The Middle And Secondary Levels: Four Mathematically Authentic Learning Experiences, Keith A. Nabb, Jaclyn M. Murawska

The Mathematics Enthusiast

This article discusses four mathematically rich settings with origins in the elementary, middle, and secondary school curricula. Depending on the questions asked and the connections made within each setting, the problem spaces allow the instructor to import tools leading to sophisticated extensions appropriate for college-level study. These topics include the Heaviside function, randomness, symmetry, modular arithmetic, the generalized Pythagorean Theorem, and the theory of groups. Given the potentially extensive ground covered by these settings, they serve to reward those students who are inherently curious while highlighting the coherence in the curriculum as one progresses through the grades. The mathematical experiences …