Popular Science Talks

2022-2023

All you need is "Computational Literacy"!

In today's world, computational literacy is an indispensable tool in every field of study that uses computers and computational technologies to solve real-life problems and scenarios. Using the mathematical thinking processes, we introduce the idea of computational literacy based on a four-step process: define the questions, reduce them to computational form, compute answers using computing software, and interpret the results. Numerous examples and interactive sites will be mentioned and discussed on in this talk.

Should you bet on it? Mathematics of gambling

Everyone told us that gambling was wrong. People realize that even though the chance of winning is very slim, the truth is - people still like gambling and betting that something will happen. Is it just a game to play to have fun? How likely is a David versus Goliath scenario in gambling? In this talk, we will discuss different games, e.g., dice, slots, blackjack and lottery and study the odds of winning them. Specifically, from the mathematical perspectives, we will discuss the pros and cons of a host-gambler relationship, e.g., winner-takes-all vs gambling away all your money.

Understanding the apportionment paradox makes you happy!

One of the most common applications in mathematics is division. For example, using the method of divide-and-choose, two persons share a candy bar or a birthday cake equally. It can be used to divide up an estate, a jewellery collection or a piece of land among heirs, to name just a few examples. In this talk, we will discuss various methods of apportionments and their paradoxes, where the word apportion is defined as "to divide and distribute in shares according to a plan". Basic math, e.g., the rounding functions, the arithmetic, geometric and harmonic means, and systematic algorithms, will help us solve the apportionment paradox, e.g., having a better understanding of the "unfairness of wanting to be fair" choices when many options exist.

(2012-2022)

Dunbar's number explains humans' friendship circle

The aim of our talk is to discuss the role of Dunbar's 5-15-50-150 model pattern in our personal social networks. This number tells us the number of meaningful and stable relationships that we can have at any one time. We also provide several social network tools for measuring and understanding our close social circle mathematically. Hence, we better understand ourselves and our relationships with family members and friends and our world.

Education? Entertainment? You are never too old to play!

Playing games is fun! Are there any theories which influence how we play games? Or can the decisions we make in games be analysed from a mathematical point of view? Game theory deals with the studying and analysis of games. In this talk, we discuss a few well-known game models, such as Prisoner's Dilemma, Chicken game, Stag-Hunt and Deadlock. Then we provide some games that we will play together during the talk and see how mathematics is involved in these games. Finally, we see how these game structures capture the characteristics of real world strategic problems.

Talk on the XOR Calculator using an artificial neural network based algorithms

As we all know, according to Boolean logic, especially in duality calculation, there are operators such as AND, OR, NOT AND, NOT OR, XOR (Exclusive OR) and NOT XOR, and only XOR and NOT XOR are non-linearly separability. To materialize and construct the two operators in a Neural Network has been a tough nut to crack. An artificial Neural Network constructed by human beings based on knowledge of the Neural Networks of their brains is a functional Neural Network, which is an information handling system that resembles the structure and functions of the human brain. In this talk, problems of linear separability and non-linear separability are solved by Multi-layer Neural Networks. In particular, our home-made XOR calculator provides an internet platform for users working to find solutions for non-linearly separable problems directly. Most importantly, we pave the way for the users who develop their own Neural Network training models for years to come.

Excuses me, How do I decide to say Yes or No when a set of events is given? The Reverend Thomas Bayes!

Bayes' theorem is named after Reverend Thomas Bayes (1701 – 7 April, 1761), who first used conditional probability to provide a prediction algorithm that is widely used in machine learning as well as artificial intelligence in the modern world. Applications of Bayes' theorem, for example, student academic performance, clinical/health/marketing decision making skills and strategies, are found in our daily lives. In this talk, we explain what Bayes' theorem is used for and why it is important to us.

In pursuit of happiness – Are any mathematical models the secret to happiness?

What kinds of metric systems measure the level of happiness, often referred to the happiness index? The treasure hunt for happiness with respect to the worldwide phenomenon depends on many factors or attributes from psychology, health, economics, social trust, well-being and more. In this talk, we briefly introduce a few latest mathematical models, for example, machine learning, social network theory and an open upward curve (the happiness curve), etc., that shape or classify a group of happy people in different countries around the globe based on how happiness is viewed. By comparing a country's society norms to other countries, we will report interesting and informative results that may surprise you and change the way we think.

The path from metrics to classifying to ranking to decision-making - Do geographical locations reflect the wealth of the worldwide stock market network?

In recent years, metric-based terms like datametrics, econometrics, finmetrics and sociometrics, just to a name few, are commonly mentioned in our daily lives. In terms of metrics, from the mathematical perspective, the Euclidean distance between two points in n-dimensional space immediately pops into our minds. Following a set of “back to basics” rules in this regard, we study a set of stock market indices as time series values. In this talk, issues with regard to the geography of the stock market will be given.

The money formula

Does the money formula exist? In this talk, we will discuss the Black-Scholes-Merton (BSM) formula, known as the money formula. Financial analysists use mathematics to advance our understanding of social-and-economic interactions/relationships as well as the development of the global economy. Can we use the BSM formula to predict the future movement of the stock market? What kind of mathematical tools do financial analysists usually use? The history of the BSM formula and several interesting facts about the BSM formula will also be mentioned and discussed in this talk.

Once upon a machine learning: how stories explain human decisions

Can machine learning (ML) improve human decision-making? In this talk, we will discuss how ML can be used to improve and understand human decision-making. ML can help us use historical data to make better human decisions, for example, business decisions, financial decisions, etc. ML algorithms discover patterns in data, and construct mathematical models using these results. Then we can use the models to make predictions on future data. Some interesting case studies will be introduced in non-technical language. In this talk, we will discuss the following interesting questions: What are the benefits of using mathematical models? What kind of mathematical tools do ML analysts usually use? Can we build ML applications at home?

Look at the world through the data

Have you ever heard of social data, marketing data, economic data and sports data? What do the numbers or the data really mean to your daily life? As Mark Twain once said, It's not what you don't know that gets you into trouble, it's what you know for sure that just ain't so. Can we use the pattern/tendency of the numbers or the data to shape and predict the future? What things get us in trouble based on the activities of the data in a daily life? In this talk, we first study how numbers rule our world and then look into some easy to use mathematical tools to answer some of the proposed questions above. In this talk, we also look at the world through the data to better reveal the myriad connections we have with the outside world, which in turn lets us learn more about ourselves from another perspective. Would you like to know more?

When social network meets matrix and computer

The talk will discuss the following: How many friends do you need in your social circle? Who is/are the most prominent person/people with respect to your friendship network? What mathematical tools can be used to calculate or measure the closeness of human relationships? What mathematical tools can reveal a person's role in a social network? How can we measure the impact of word of mouth? In this talk, we will introduce two types of tools, which can contribute social network related research. These two types of tools are: (1) mathematical tools (counting and matrices) and (2) computer visualization tools. Then we will discuss some concrete applications of these tools. For example, how do you use these tools to illustrate one abstract concept -- "the importance of social networks"? How do you use these tools to describe the evolution of a given network, such as the change of a person's friend-network or the expansion of a bad gang? Through these examples, we try to bring you a new perspective on social networks.

Several ways of expressing the constant e

e = 2.71828182845904523536028747135266249775724709369995...

One of the well-known constants, besides π, is the constant e that is the base of the natural logarithm. Its symbol e honors a Swiss mathematician, Leonhard Euler (1707-1783). The constant e is sometimes known as Napier's constant. In this talk, we will summarize the derivation of the constant e as many ways as possible. Highlights are an exponential function is equal to its own derivative, deriving from integration, a famous sequence relating to e, a relationship between e and the continued fraction, e and a recursive formula, etc.

Who cares about the logistic equation?

The logistic growth equation is one of the most famous equations of the past few decades. The logistic function finds applications in a wide range of fields, including artificial neural networks, biology, ecology, biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, and statistics. In this talk, we will explore the logistic growth model and its modification. Deterministic logistic equations in continuous time and in discrete time are introduced. The logistic map and its behavior are mentioned.

Applications of dynamic programming problems to sequence alignment and hidden Markov models

Dynamic Programming was introduced by Richard Bellman and George Dantzig in the year 1952. Initially, it was known as stochastic linear programming. It is a mathematical technique to solve a wide range of decision-making problems. Many decision-making problems involving a process in which several stages take place work in such a way that, at each stage, the progress is independent of the strategy used for solving the problems. This type of multi-stage process problems is known as a dynamic programming problem (DPP). Mathematically speaking, a DPP is a decision-making problem in n variables, the problem being subdivided into n sub-problems (segments), with each sub-problem being a decision making problem in one variable only. The solution to a DPP is achieved sequentially, starting from one (initial) state and moving to the next, until the final stage is reached. In this talk, we will explore two major classes of applications of DPP's: Sequence Alignment and Hidden Markov Models. Many aspects of the DDP's can be understood by using simple algebra and pre-algebra skills.

Interpolation of Colors

What are the concepts involved in the interpolation of colors? When interpolating colors, we must somehow define which colors are in-between, say, what is the color half-way between red and green? In computer graphics, colors are represented in a color space, and the geometry of this space implicitly answers this question. However, there exist a lot of color spaces, and different color spaces can yield different results. We will look at two color spaces, the RGB (red, green, and blue) and HSV (hue, saturation, and value) color spaces. In this talk, we will explore two major classes of color interpolation: the RGB interpolation and the HSV interpolation. How a colorful picture can be described by a simple interpolation formula is explained.

Let us get to know Nicolas Bourbaki

In August 2008, Nicolas Bourbaki was denied membership in the AMS (the American Mathematical Society); he is the only mathematician known to be denied membership. Bourbaki was a member of the Societe Mathematique de France and applied for reciprocal membership. Bourbaki, however, was denied membership in the AMS, basically on the grounds that Bourbaki was neither an individual nor an institution. Who is Nicolas Bourbaki? What is the major contribution of Nicolas Bourbaki's work to the mathematical community? The story of Nicolas Bourbaki is rich and full of mystery. In this talk, let us explore the history of a group of (mainly French) 20th-century mathematicians who had close ties to Nicolas Bourbaki.