(Click on title to view those with video.)
The Hungarian Algorithm: A Solution to the Assignment Problem
Brian Hadley (1/29/15)
In this talk we will discuss the Assignment Problem: How do we optimize the assignment of employees to work tasks? The problem of assigning "individuals" to perform specific "tasks" has special characteristics and structure, which were cleverly exploited by Harold Kuhn in 1955 to produce an efficient method that generated an optimal solution. We will work out examples of the "Hungarian Algorithm," work together to solve the Assignment Problem, and examine Kuhn's paper describing his remarkable method.
A Quest to find a One-to-One and Onto function from the line segment [0,1] to the square plane region [0,1]x[0,1]
Alejandro Saldivar (11/20/14)
Many theorems in mathematics address the existence or non-existence of mathematical objects such as solutions to equations; however, finding an actual and precise mathematical object can be an exciting and, at times frustrating, quest. In this seminar we will talk about one-to-one and onto functions between sets, and the challenges involved in finding a one-to-one and onto function. Along the way, we will discuss decimals extensively.
100 Years of Mathematics at GRJC/CC
John Dersch (10/15/14)
In Fall 1914 the GRJC Mathematics Department offered one math class, taught by one instructor to fewer than twenty students. One hundred years later we offer 22 courses, taught by approximately 75 faculty to more than 5000 students each semester. We’ll discuss the people and courses that got us to where we are today. Emphasis will be on personalities, course development and anecdotes.
Mathematics in the World of Industrial Engineers
Duy Duong-Tran (9/18/14)
The influence of mathematics in our society is amazing. For example, mathematics plays a role in the infrastructure of the automobile industry (aerodynamic simulation through the use of math modeling), bioengineering (footwear design through piecewise linear interpolation and modeling), and the aviation industry (cubic spline interpolation at Boeing Research and Development to replace “lofting” technique).
This seminar will discuss the use of mathematics in the world of industrial engineering. Specifically, we will talk about Optimization Problems in the industry using Linear Programming (LP). Surprisingly enough, LP problems often do not employ any computer algorithm techniques, and most mathematics students are exposed to LP problems early in their careers without an official introduction to the topic. Well-known LP techniques can be applied to scheduling, transportation, assignment, capacity planning, network optimization models, project management, facility planning, and capital budgeting problems.
All of these reside under the applied mathematics field called Operations Research (OR). We will go through the technique of solving a couple of problems, and will be surprised at how much impact OR (or more generally mathematics) has upon the success of a manufacturing based corporation.
One Aspect of Universal Design: Playing Games in Math Class
Monica Stevens and Barb Bouthillier (4/15/14)
In an effort to engage all learners, in particular, kinesthetic learners, we collected and developed activities designed for instruction and practice in our Basic Math courses. These activities can be adapted for elementary or secondary use, or even for higher level classes. During this presentation, we will explain the process we used to create the activities, their implementation, and the results. Participants will play multiple activities and copies of them will be available electronically.
Same Results, New Approach
Andrea Hayes (3/17/14)
Basic mathematical operations such as addition, multiplication, division, and subtraction are now being presented to elementary school children using algorithms that are different than the traditional ones that many of us are used to. This talk will look at some of these different methods of computing sum, product, quotient, and difference, as well as discuss why these methods are being taught to students and how they may actually help with number sense and mathematical comprehension.
“omg - i have to take a Mental Abuse To Humans class”
Pat Bentley and Erin Burke (2/19/14)
Why do so many college students need remedial math? Why do so many of those students then continue to struggle with the subject? Why does the thought of even having to take a math class cause immediate anxiety? Two math teachers taught an Introductory Algebra course at a unique summer program through Ferris State University that was designed to combat those specific problems. During this seminar, they will share some of their strategies for teaching remedial math at the college level, emphasizing reading and writing in the discipline.
Mersenne Primes and Perfect Numbers: A Love Story
Dan Garbowitz (1/22/14)
Perfect numbers were known to the Greeks and have been studied since at least the 3rd century B.C. Marin Mersenne, a 17th century theologian and mathematician, developed a list of prime numbers, all with the same interesting form. Sometime later, Leonard Euler proved a fascinating statement that related the perfect numbers to the Mersenne Primes. During this seminar we will investigate this theorem in particular, and other number theory topics relating perfect numbers and Mersenne Primes.
"Significant Figures: The Mathematics Behind their Significance. "
Dana Sammons (12/05/13)
Significant Figures are
- those digits that carry meaning contributing to its precision (Wikipedia)
- the number of important digits in an expression (Whatis)
Just as many people believe what they read on websites like Wikipedia and Whatis when it might not be justified, often people believe that numbers are significant without carefully considering whether they deserve it.
In “The Pedagogy of Poverty vs. Good Teaching,” M. Abraham suggests we should provide students with a meaning-driven curriculum. If we are to analyze, discuss and interpret the meaning of the results of calculations with any integrity, we must know with what precision we should assign the numbers.
This talk will look into the mathematics behind the “rules” associated with significant figures, including some of the suggested improvements people have made over time.
"What's My Line?"
Tom Neils (11/13/13)
Many scientific experiments are carried out to determine the mathematical relationship between two or more variables. Graphing the experimental data is often the most effective way of finding this mathematical relationship, because one can determine a curve of best fit for the trend in the data and also obtain a visual of the relationship between the variables. During this interactive seminar we will discuss the extent to which chemists will go to obtain a linear fit for their data and get some practice fitting the slope-intercept formula to various data sets.
Old News About Percentages
Radu Teodorescu (10/17/13)
Everyone has heard of percent. Beginning with pre-algebra, it is taught at GRCC in a variety of courses. Many of the current methods for teaching percent problems have been used for decades. This talk will submit an idea slightly different from traditional concepts. Some may agree with it, many others may have reservations and even objections. However, it is hoped that many in the audience will be surprised by some of the interpretations revealed during the talk.
Nancy Forrest (9/16/13)
The Chinese abacus has been used to calculate and record numbers for over nine hundred years. This introduction to its use will include an overview of the rich history, as well as instruction on how to perform basic mathematical operations. There will be a hands-on opportunity to use the abacus … no batteries needed!
Teaching Developmental Mathematics: It's Not Just About Math!
Betsy McKinney, Andrea Hayes, Shanna Goff, Linda Spoelman, Dominic Mattone and Paul Miltgen (4/23/13)
Across the state and the country, the need for developmental mathematics courses is growing as more students are entering college underprepared. These students bring a unique set of challenges, skills, and experiences to the classroom. After a brief overview of current trends in developmental education, a diverse panel of experienced developmental mathematics teachers will discuss the various challenges they encounter when teaching the developmental student. Topics will also include best practices in the developmental classroom, technology in the developmental classroom, and the “other” skills developmental educators teach their students. Time will also be given for the audience to ask questions of the panel.
Catastrophic Electrical Damage took place - let’s check the Math to see why!
Roger Berry (3/19/13)
All protection from damage or injury due to electrical faults begins with determining the amount of potential fault current. Mechanical and thermal energy released in less than 4 milliseconds can produce catastrophic results. Electrical equipment and protective devices must be tested and rated to withstand the potential forces involved.
Electrical designs are evaluated for worst-case conditions to insure that equipment and people are adequately protected. Fault currents on both sides of the decimal point can result in destructive forces. Short circuits can result in destructive currents over 200,000 amps producing a blast that results in equipment damage and potential injury to personnel due to flash burns and sound, while ground faults as low as five milliamps can produce fibrillation resulting in death. In addition, lower level arcing faults can destroy electrical equipment or start a fire.
How do we do the math?
Counting with Polynomials
Sang Lee (2/20/13)
Do we obtain any valuable information from the product of polynomials? Specifically, what do coefficients and exponents tell us when polynomials are multiplied? In this talk, we introduce a counting technique that utilizes the coefficients and exponents in the product of polynomials. We then examine some counting problems such as determining the number of ways for different routes, muffin orders, changing a dollar, solutions to an equation, and partitions of an integer.
What's Math Got to Do with It?
Yumi Watanabe (12/05/12)
In this talk we will explore the world of mathematics. Beginning with our ability to sense quantities, we will survey various aspects of ideas and concepts that make up the world of mathematics, including numbers, algebra, calculus and areas of modern mathematics. Along the way we will ask and attempt to answer questions such as, "What is mathematics, anyway?", "What is it good for?", "Why is it so hard?" and "Does mathematics have anything in common with disciplines such as language arts and social sciences?" At the end of the talk, borrowing words of Sir Isaac Newton, a definition of mathematics (perhaps an unconventional one) will be given.
Brian Hadley (12/05/12)
Magic squares have fascinated professional mathematicians as well as mathematical hobbyists for over 4000 years. The Lo Shu magic square with its uniqueness captures the symmetry and beauty of mathematics, Dürer's square backdrops his famous engraving Melancholia, and Benjamin Franklin constructed them to keep his mind sharp. We will explore a few magic squares and unlock some of their mysteries.
Paradoxes: What Are They and Why Are They Significant?
Patrick Campbell (11/13/12)
Consider the following statement: “This sentence is false.” Well then, if the statement is true, it must be false; and if the statement is false, then it must be true. What is going on here? The statement above is a version of the “Liar” or “Epimenides Paradox”, named after the ancient Greek Epimenides of Crete, who is believed to have once stated that all Cretans are liars. As interesting and puzzling as paradoxes of this sort may be, even more fascinating things arise when we investigate the paradoxes of mathematics and logic. In this seminar, we will look at some paradoxes relevant to mathematics and logic, attempt to understand what it is that creates such bizarre results, and discuss why paradoxes are significant mathematically, historically, and philosophically.
To Infinity and Beyond
Kelly Rozin (10/23/12)
A great poet, William Blake, once wrote, "To see the world in a grain of sand, and see heaven in a wild flower, to hold infinity in the palm of your hands, and eternity in an hour." One might think that these words are silly a paradox that can never exist, but others might think it’s possible. Can you really hold infinity in the palm of your hand? Is it tangible? Does it exist? This talk will go into the discovery and history of infinity and what it actually means to be infinite. It will also describe the different methods of proving infinity's existence and how it is used in the world of mathematics and our everyday lives.
50 Centuries in 50 minutes (A Brief History of Mathematics)
John Dersch (9/19/12)
How did we get the mathematics that is studied today? Who was responsible for major advances in the mathematics that we now take for granted? When and where did this work take place? Such questions will be addressed by tracing the development of mathematics from 3000 B.C. to the dawn of the 21st century. There will be time for questions and suggestions for further study will be made.
Number Theory Potpourri
Tom Post (4/18/12)
This informal talk will feature a collection of interesting topics from the branch of mathematics called number theory. Topics of discussion will include Collatz’s Sequence, the Golden Ratio, Fibonacci Numbers and Binet’s formula, Pythagorean Triples, Continued Fraction Expansions, and Solutions to Pell’s Diophantine Equation.
Fractals and Chaos
Julia Moore and Tom Worthington (3/22/12)
Beyond their captivating images, why are fractals so interesting to mathematicians? The answer comes from their unique history, recent discovery and their many interesting properties of symmetry, simplistic complexity and self-similarity. Fractals are very different from the lines and curves created by most simple equations, yet these complex graphs come from very basic functions that only reveal their complexity as they are recursively applied. Many mathematicians believe they may be used as a way of predicting seemingly "random" events in the natural world, and their applications have greatly improved the advances of the field known as Chaos Theory.
For the talk, bring in your TI-83 or TI-84 calculators and get programs that combine Newton's Method with fractals.
Teaching Methods that Encourage Participation
Julia Moore and Melanie Forbes (2/21/12)
Julia Moore and Melanie Forbes will discuss high (and low) - tech methods for keeping your students involved in the classroom. Discover the free online graphing software of Geogebra, and explore the creation of a community of mathematics teachers and students using Geogebra at GeogebraTube. Listen to a unique perspective on using whiteboards in the classroom as a teaching tool. Delve into the free software of Respondus and Studymate that can create Flash-cards, Quizzes and Jeopardy games that can be used as study tools for your classes.
Buddha loves geometry… at least according to Japanese?
Wayne Hsieh (1/25/12)
Sangaku (or San Gaku) are Japanese geometric puzzles carved on wood tablets that are used as offerings at Shinto shrines or Buddhist temples. The puzzles consist of circles and triangles utilizing concepts from Euclidean geometry, and they typically ask the solver to find the relationship between the circles and triangles.
In this particular Sangaku, we will be looking at three circles placed inside a particular right triangle, and will investigate the radii and areas of the circles.
Why People Trust Statistics
Steve Harris (12/7/11)
Many students in an introductory Statistics course sail along fine until “Distribution of a Sample Mean” sinks their boat. After failing to find an illustration that explained the concept in a way I could use with both math-oriented and non-math-oriented students, I built my own. The result is an Excel spreadsheet that visually demonstrates the power of the Central Limit Theorem.
By changing any of these variables – population range, population size, sample size, number of samples – you can watch the conclusion of the Central Limit Theorem develop before your eyes. This little app has proven quite useful in helping students understand why we’re willing to make significant decisions based on a small amount of sample data, and reinforces why the Central Limit Theorem indeed is central in the field of Statistics.
Euler’s Formula for Polyhedra: The Second Most Beautiful Theorem in Mathematics
Dan Garbowitz (11/16/11)
Euler’s formula for polyhedra is so simple that a grade school student can understand it, yet this simple formula remained hidden from mathematicians and great thinkers for over 2000 years! The results of the formula gave birth to a new branch of mathematics called topology. This talk will focus on the history of Euler’s formula and present two proofs of it. The proofs differ vastly in their arguments and each is quite beautiful. One will even use a second branch of mathematics that Euler is responsible for – graph theory.
Mathematics is with me every time I shift
Brian Deurloo (10/19/11)
In the world of manufacturing and design, mathematics is the backbone which governs the systems we build for use in the real world. As an engineer it is essential to understand how these theoretical models perform so that each design can be optimized to ensure flawless function in the presence of the many noise factors from manufacturing.
In this presentation we will look at the theoretical "nominal" design of an automatic transmission shift system through the eyes of the trigonometry and algebra that governs it. Synchronization of these "cord length" travels between the shift lever and transmission lever are critical to all of the aspects of the shift system function. Finally, we will use some computer generated normally distributed statistical distributions to add in the variability of the system components to understand how to bring the theory into real world practice.
Dynamical Systems, Andrei Markov, and the Stochastic Matrix
Brian Hadley (09/20/11)
In a system with a finite set of variables we can use the powerful tool of a Stochastic Matrix to examine how the state of a dynamical system will change with time. It was the Russian mathematician Andrei Andreyevich Markov who set the groundwork for a completely new branch of probability theory, and launched the theory of the stochastic processes. Today stochastic processes are used to study social sciences, physics, biology, economics and differential equations. We will examine simple dynamical systems utilizing the stochastic matrix, and take a look at practical applications of stochastic processes.
Mathematical Modeling and Electrical Engineering
Sam Schoofs (02/23/11)
Electrical engineers use a wide range of mathematical models to represent the physical realities of voltages and currents in electrical circuits. This talk will focus on models of electrical circuits that use calculus, differential equations, and linear algebra. Some models from the field of telecommunications will also be discussed.
Check Digit Schemes: An Application of Number Theory
Sang Lee (01/26/11)
Identification numbers are used to represent products, accounts, documents or individuals. Since we (our society) rely heavily on identification numbers to transmit information, sooner or later a transmission error will occur. Thus, it is crucial to know when an identification number has been transmitted incorrectly. The check digit schemes are the mathematical methods that detect when the identification numbers have been transmitted incorrectly. In this talk, we will look at a few check digit schemes that are used currently and the mathematics behind them.
Quaternions and Rotation Sequences
Kurtis Bell and Ryan Mammina (12/10/10)
Consider a remote object in 3-dimensional space of which we wish to track at a point in time. It is reasonable to ask, what is the most efficient way for one to track such an object? The topic of this talk, quaternions, will give us the tools we need to answer the aforementioned question. We will begin this survey of an introduction to hyper-complex numbers and their origin. The goal of the talk will be to provide a comparative analysis of two different methods for tracking the said object. With this in mind, the audience will make the final conclusion as to which method is most efficient. Join us as we venture into the curious world of quaternion geometry.
The Mathematics of Sliding Logs (A presentation on the development, use, and secrets of the slide rule.)
Roger Berry (11/18/10)
This presentation will provide an understanding of how the slide rule performs mathematical calculations, and a working knowledge of its application as a precision instrument. A working model will be provided for attendees which will allow you to go "Slip Slidin' Away" to solve future math problems.
We will review the use of logarithms, or logs as they became known, to do complex calculations. The use of logarithm tables and the amazing leap to simplified use through sliding rules culminated in the slide rule as we know it today. Great advances in science took place between 1700 and 1970 as the slide rule was used to do multiplication, division, logs, roots, exponential values and trigonometric functions.
The Mathematics of Apportionment (How the first president of MAA teamed with a U.S. Census Bureau Chief Statistician to take on Thomas Jefferson, Alexander Hamilton, James Dean, and Daniel Webster.)
Dana Sammons (10/20/10)
This talk will introduce various methods used to make "fair" apportionments. Then we will discuss the methods used throughout the history of the U.S. to decide how many representatives each state should have in Congress. We will also try to address the question whether the current method is biased.
What Is This e Thing?
John Dersch (9/22/10)
The common answer that "e is approximately 2.718" says little about the nature of one of the most important numbers in mathematics. This talk will begin by examining numerical and geometric interpretations of e. We will then look at a proof of the irrationality of e (short and sweet), briefly outline a proof that e is transcendental (the full proof is really sweet but not short – an opportunity to experience a complete proof will be offered), and end with a discussion of the tantalizing question "Is e normal?" (sweetest of all, but maddeningly frustrating...).
Tom Post (4/21/10)
Some of us are a part of a generation that never were faced with making a calculation without a use of a hand-held calculator. As a result, many of the mental techniques in making either exact or approximate calculations have been lost to technological advances. This is not to disagree with the use of calculators (I literally love my calculator), but only to bemoan what seems to be lost at the expense of our progress. Memory work, normally expected in our grade schools, has diminished to the point where students in our college mathematics courses don't know their times tables. Lack of that fingertip information is the prime cause of frustration and failure in the elementary pre-algebra courses that now dominate, in number, the math courses that are taught as college courses.
This talk is meant to introduce the average math students a new way of approaching the task of mathematical calculations as well as to inspire the more advanced students by integrating algebraic techniques with these calculations without the use of the calculator.
Extensions to Complex Numbers of Some Common Functions
Radu Teodorescu (3/18/10)
After a succinct presentation of complex numbers, we will extend to complex numbers the exponential, trigonometric and logarithmic functions. How this extension is done, several new properties of these functions, and some unexpected implications will also be presented.
What Happened in Vegas... (Probabilities and Expected Values Associated with Texas Hold'em)
Jennifer Borrello (2/17/10)
The AMATYC (American Mathematical Association of Two-Year Colleges) Conference held in Las Vegas, Nevada in November of 2008 had several interesting presentations about probability. This talk will focus on the card game Texas Hold'em. There will be a brief introduction to the game followed by a discussion of the probabilities and expected values associated with starting hands.
Rational Approximations of Square Root of 2 (An Introduction to Isosceles" Almost" Right Triangles)
Dave Friday (1/21/10)
While visiting the Calculus and Physical Sciences Tutorial Lab last semester, a question was posed: for what value of n will the sum of the first positive n integers be a perfect square? A thorough investigation of the problem and the introduction of the concept an isosceles "almost" right triangle yielded a number of interesting results. One of the results involves a sequence of rational numbers that converges to square root of 2, yielding some excellent approximations.
The Gamma Function and Other Neat Mathematical Things
Radu Teodorescu (11/12/09)
In this presentation, we will talk about multiplication, or to put it another way, many kinds of products. The expression n! (read n factorial), the product of all integer numbers starting with 1ending with n, makes sense only for positive integers 1,2,3, ... The main topic of the presentation is how to define the n factorial function for non-integer numbers. This problem, solved almost three hundred years ago by Leonhard Euler, still keeps busy many mathematicians with its implications and open questions.
Want To Teach Math?
Panel Discussion (10/21/09)
Panelists: Dan Garbowitz, Donna Joseph, Gary Kemp, Marsha Potter, Jim Vidro
Are you thinking about teaching mathematics? Are you teaching mathematics currently at GRCC and ever wonder what it's like to teach mathematics in high schools or middle schools? This seminar is a panel discussion on teaching (primarily secondary) mathematics, intended for those who are interested in pre-college mathematics education. The panelists consist of current or retired high school math teachers who are willing to share their experiences in order to benefit future (and current) math teachers. If you are interested in teaching mathematics, come find out what they have to say! We hope to leave time at the end of the seminar to take questions from the audience.
Sang Lee (09/16/09)
A regular polyhedron is a 3-dimensional convex solid in which all faces are congruent polygons, and the same number of polygons meet at each vertex. The Greeks, especially Plato and his followers, studied these solids to such an extent that they became known as the "Platonic solids". Furthermore, the Greeks believed that there are only five regular polyhedra. However, in a recent publication of Math Horizons (by MAA), it declared that "A new Platonic solid has been discovered!" Did the Greeks overlook the 6th regular polyhedron? In this talk we investigate the number of regular polyhedra using Graph Theory.
Gary Slopsma (04/22/09)
How can a person contemplate infinity? It may seem beyond human grasp, yet there exist mechanisms by which we may decipher the mysteries of the infinite. This talk will introduce some of these mechanisms, sauntering through history, set theory, and some concepts of functions along the way. We will conclude with some startling and mind-bending results regarding the size(s) of infinity.
Puzzling Mathematics of Sudoku
April Russell (03/18/09)
Sudoku is the latest craze in puzzles, and is played by entering digits from 1 to 9 to complete a partially filled 9 x 9 grid so that each digit appears exactly once in each row, column, and 3 x 3 sub-grid. There are numerous variations with additional restrictions, for example, Sudoku X, where the entries on each of the main diagonals are also distinct. In this talk, the results of my summer research on Sudoku variations will be presented, using permutations, rook polynomials, and equivalence relations.
Tom Post (02/19/09)
Just as Maclaurin or Taylor series are used to represent continuous functions with an infinite series of polynomials, a Fourier series is used to represent a periodic function in terms of an infinite sum of sines and/or cosines. Since sine and cosine functions represent simple harmonic motion (pure tones), Fourier series become a very useful tool in analyzing more complicated wave forms such as those produced by musical instruments, showing that any periodic wave form can be reduced to a superposition of pure tones of varying levels of magnitude(modal analysis). To determine these levels, called Fourier coefficients, we make use of the orthogonal relationships of the sine and cosine functions. We will look at the methods used to determine these coefficients and also display some of the interesting mathematical identities that result.
The Doomsday Algorithm – Need I Say More?
Tom Worthington (01/21/09)
You know your own birthday, but do you know what day of the week you were born? What about historical events? What day of the week did they take place? The doomsday algorithm gives you a way to calculate the day of the week of any given date based on the Gregorian calendar. Come find out how this works!
The Fastest Curve
Christopher Grow (12/11/08)
If you were to slide an object down a ramp, what curve will get it to the bottom the fastest? The answer to this question, posed by Johann Bernoulli in 1696 as a challenge to the mathematical community– Isaac Newton, in particular – is called the brachistochrone and it is the topic of our discussion. We will explore Bernoulli's result and its connection to a different problem: If you were to slide an object down a ramp, what curve will get it to the bottom in the same time regardless of where you start it?
How Do Calculators Calculate? - A Look at the CORDIC Algorithm -
Curt Baragar (11/13/08)
How does your calculator know the answer to sin(13.873°) or ln(8.2)? You may be surprised to learn that modern calculators rarely use polynomial approximation techniques such as Taylor series. Instead, they rely on an algorithm developed in 1959 for use in navigational computers on the B-58 bomber aircraft. In this talk we will explore the CORDIC (COordinate Rotation DIgital Computer) algorithm used by handheld calculators from Texas Instruments, Hewlett-Packard, and others.
Competitive Math: How to Become a Mathlete
David Friday (10/16/08)
The purpose of this talk is to help encourage awareness of and desire to take the AMATYC Student Mathematics League exam through exposure to the different types of competitive math that exist. This talk will cover what competitions are out there and available to students, particular problems from previous competitions, problems from previous SML exams, and a general strategy for the competition itself. In addition, a short interview with a previous SML winner and GRCC student will help to answer questions students may have about getting involved.
What's the Point?
John Dersch (09/18/08)
Most of us take decimal fractions for granted and may think of them as nothing more than advice for simplifying computations. Indeed that was the primary reason they were developed, but a close look reveals that they influenced 17th century mathematicians' understanding of number, variable, the continuum and the development of calculus. In this talk we begin with the calculus of Newton and Leibniz, then travel back to the analytic geometry of Fermat and Descartes, ending at Simon Stevin's 1585 publication "L'arithmétique" and its appendix "De Thiende" (The Art of Tenths), with side trips to contributions from the Greeks, the Arabs and wherever else the road takes us.
Generalized Binomial Coefficients and Modified Pascal's Triangle
Elliot LaForge (04/09/08)
This talk begins with a quick review of sequences. In terms of sequences, some of the interesting patterns in Pascal's triangle will be explored. Beginning from the well-known relationship between Pascal's triangle and the coefficients in the binomial expansion of (x+y)n, more general binomial theorems will be investigated and derived. (The results in this talk were discovered by Elliot Laforge.)
Curvatures of Surfaces – Why I Love Gauss
Yumi Watanabe (03/19/08)
Curvatures of surfaces are quantities that describe how "curved" a surface is at each point. How do we quantify these? This notion will be developed from the similar notion in curves, highlighting the great contributions of Carl Friedrich Gauss in the area of mathematics called differential geometry. The talk will end with truly amazing theorems in differential geometry due to Gauss.