ESP Biography
VIVEK KAUL, Data Scientist with mathematical background
Major: Electrical and Computer Engineer College/Employer: The Young Socratics Year of Graduation: 2010 

Brief Biographical Sketch:
I graduated in 2010 with a PhD in Electrical and Computer Engineering from Georgia Tech, Atlanta. I also have Masters degrees in Mathematics, Computer Engineering and Aerospace Engineering from Georgia Tech and I did my undergraduate studies in Indian Institute of Technology (IIT) Bombay. I am interested in conceptual understanding and teaching of mathematics and the physical sciences. Past Classes(Clicking a class title will bring you to the course's section of the corresponding course catalog)P4853: The Galileo Affair in Splash Spring 2016 (Apr. 09  10, 2016)
"Future centuries may find it strange that after he retracted an opinion which had not yet been absolutely prohibited in public... so much rigor should be used against a pitiable old septuagenarian as to keep him in a (private if not public) prison: he is not allowed to return to his city and his house, or to receive visits and comfort from friends. He has infirmities that are almost inseparable from old age and require almost continuous assistance.... This shook my heart and drove me to tears, as I considered the vicissitudes of human affairs and the fact that he had had so many uncommon honors and accomplishments, whose memory will last for centuries." (December 5, 1634, Peiresc's plea for a pardon)
In 1633, the Roman inquisition condemned Galileo as a suspected heretic for defending Copernicus's hypothesis of the earth's motion, and denying the scientific authority of Scripture. This incident is the most cited one in the history of sciencereligion interactions. Does the trial of Galileo epitomize the conflict between enlightened science and dogmatic religion? We will go beyond the simple narratives of that story to look deeper into the scientific, religious, philosophical and personal issues at stake in this controversy, based on what the original documents and letters say.
Note: This is a history of science class, not a regular science class.
P4854: The Shape of the Earth in Splash Spring 2016 (Apr. 09  10, 2016)
"Is there anyone so senseless as to believe that (on the other side of the earth) there are men whose footsteps are higher than their heads?... That crops and trees grow downwards? That the rains and snow and hail fall upwards to the earth?" (Lactantius, 4th century CE)
There was a time when people across different cultures believed that the earth was more or less flat, not because they were stupid in any way, but because reasoning by common sense led them to it. Even many of the best philosophers in ancient Greece adhered to some version of a flat earth viewpoint. How did some of the philosophers (or 'scientists' of the time) begin to claim that the earth was spherical? What observations and arguments led them to it? In this course, we will imagine travelling back in time to the ancient world, two thousand years before the advent of modern science, and understand how educated people convinced themselves and the others that the earth was really spherical, without satellite pictures and the ability to circumnavigate the world. We will look at the mixture of right and wrong arguments offered by the key philosophers and astronomers of the time, including Aristotle and Ptolemy. Along the way, we will also understand the physics of Aristotle (which was the dominant physics for 2000 years), and the ancient astronomical explanations of eclipses and the phases of the moon.
Note: This is a history of science class, not a regular science class.
P4855: Great ScientistsKepler in Splash Spring 2016 (Apr. 09  10, 2016)
Want to know how we moved from a geocentric model to the heliocentric model of the universe? Did you know the person after whom NASA named one of their space shuttle? Learn about the key scientific figure, Kepler, who was instrumental in putting the heliocentric model of Copernicus on firm ground. In this course, we will see how his tenacity and perseverance led to development of his three laws of planetary motion that inspired Newton’s universal of gravitation. Along the way, we will look at his legendary tussle with Tycho Brahe without whose observations Kepler could not have made much headway in his theories. We add to this, his work in explaining human vision and behavior of telescopes and his work on logarithms. And we will look at Kepler and his times, how his religious beliefs influenced his writings, how he devoted as much time to astrology as to astronomy and much more.
P4856: Great ScientistsNewton in Splash Spring 2016 (Apr. 09  10, 2016)
Considered by some to be the greatest “scientist” (natural philosopher would be the word used back then!) of all time, Newton shaped the modern world in ways too numerous to mention. In this course, we will go through his most important contributions: the laws of optics, the binomial theorem, integral and differential calculus, laws of motion and above all his crowning glory, the universal law of gravitation. But we won’t stop there! We will also discuss his other “outlandish” interests like alchemy and iconic fights with contemporary scientists like Leibniz and Hooke that divided continental Europe and England. Let us embark on the journey to understand the complete man that Newton was: a loner, a genius, a celibate, a heretic and a bitter critic of his rivals and the first person in England to get state funeral whose attainment lay in the realm of the mind.
P4570: The Shape of the Earth in Splash Fall 2015 (Nov. 07  08, 2015)
"Is there anyone so senseless as to believe that (on the other side of the earth) there are men whose footsteps are higher than their heads?... That crops and trees grow downwards? That the rains and snow and hail fall upwards to the earth?" (Lactantius, 4th century CE)
There was a time when people across different cultures believed that the earth was more or less flat, not because they were stupid in any way, but because reasoning by common sense led them to it. Even many of the best philosophers in ancient Greece adhered to some version of a flat earth viewpoint. How did some of the philosophers (or 'scientists' of the time) begin to claim that the earth was spherical? What observations and arguments led them to it? In this course, we will imagine travelling back in time to the ancient world, two thousand years before the advent of modern science, and understand how educated people convinced themselves and the others that the earth was really spherical, without satellite pictures and the ability to circumnavigate the world. We will look at the mixture of right and wrong arguments offered by the key philosophers and astronomers of the time, including Aristotle and Ptolemy. Along the way, we will also understand the physics of Aristotle (which was the dominant physics for 2000 years), and the ancient astronomical explanations of eclipses and the phases of the moon.
Note: This is a history of science class, not a regular science class.
P4571: The Galileo Affair in Splash Fall 2015 (Nov. 07  08, 2015)
"Future centuries may find it strange that after he retracted an opinion which had not yet been absolutely prohibited in public... so much rigor should be used against a pitiable old septuagenarian as to keep him in a (private if not public) prison: he is not allowed to return to his city and his house, or to receive visits and comfort from friends. He has infirmities that are almost inseparable from old age and require almost continuous assistance.... This shook my heart and drove me to tears, as I considered the vicissitudes of human affairs and the fact that he had had so many uncommon honors and accomplishments, whose memory will last for centuries." (December 5, 1634, Peiresc's plea for a pardon)
In 1633, the Roman inquisition condemned Galileo as a suspected heretic for defending Copernicus's hypothesis of the earth's motion, and denying the scientific authority of Scripture. This incident is the most cited one in the history of sciencereligion interactions. Does the trial of Galileo epitomize the conflict between enlightened science and dogmatic religion? We will go beyond the simple narratives of that story to look deeper into the scientific, religious, philosophical and personal issues at stake in this controversy, based on what the original documents and letters say.
Note: This is a history of science class, not a regular science class.
P4584: Great Scientists: Kepler in Splash Fall 2015 (Nov. 07  08, 2015)
Want to know how we moved from a geocentric model to the heliocentric model of the universe? Did you know the person after whom NASA named one of their space shuttle? Learn about the key scientific figure, Kepler, who was instrumental in putting the heliocentric model of Copernicus on firm ground. In this course, we will see how his tenacity and perseverance led to development of his three laws of planetary motion that inspired Newton’s universal of gravitation. Along the way, we will look at his legendary tussle with Tycho Brahe without whose observations Kepler could not have made much headway in his theories. We add to this, his work in explaining human vision and behavior of telescopes and his work on logarithms. And we will look at Kepler and his times, how his religious beliefs influenced his writings, how he devoted as much time to astrology as to astronomy and much more.
P4585: Great Scientists:Newton in Splash Fall 2015 (Nov. 07  08, 2015)
Considered by some to be the greatest “scientist” (natural philosopher would be the word used back then!) of all time, Newton shaped the modern world in ways too numerous to mention. In this course, we will go through his most important contributions: the laws of optics, the binomial theorem, integral and differential calculus, laws of motion and above all his crowning glory, the universal law of gravitation. But we won’t stop there! We will also discuss his other “outlandish” interests like alchemy and iconic fights with contemporary scientists like Leibniz and Hooke that divided continental Europe and England. Let us embark on the journey to understand the complete man that Newton was: a loner, a genius, a celibate, a heretic and a bitter critic of his rivals and the first person in England to get state funeral whose attainment lay in the realm of the mind.
P4327: The Shape of the Earth in Splash Spring 2015 (Apr. 11  12, 2015)
There was a time when people across different cultures believed that the earth was more or less flat, not because they were stupid in any way, but because reasoning by common sense led them to it. Even many of the best philosophers in ancient Greece adhered to some version of a flat earth viewpoint. How did some of the philosophers (or 'scientists' of the time) begin to claim that the earth was spherical? What observations and arguments led them to it? In this course, we will imagine travelling back in time to the ancient world, two thousand years before the advent of modern science, and understand how educated people convinced themselves and the others that the earth was really spherical, without satellite pictures and the ability to circumnavigate the world. We will look at the arguments offered by the key philosophers and astronomers of the time, including Aristotle and Ptolemy. Along the way, we will also understand the phases of the moon, and how the ancients inferred that eclipses are caused by the alignment of the sun, moon and the earth.
Note: This is a history of science class, not a regular science class.
M4332: The Art of Summation in Splash Spring 2015 (Apr. 11  12, 2015)
Summing the numbers from 1 to 5 can be done quickly. Summing the numbers from 1 up to 100 would take a lot more time. Or is there a quick way to do it? How about the general problem of summing the first N numbers? Drawing inspiration from Pythagoras and his followers, and a precocious elementary school kid who grew up to become the "Prince of Mathematicians", we will discover a number of different approaches to the problem. We will generalize those approaches to compute the sum of an arithmetic series and geometric series. We will also play with other summations: summing the first N squares, or the first N cubes, and try to discover connections between these different series.
We will follow bacteria as they grow and divide, and ask why they don't conquer the world. We will trace back a children's nursery rhyme in English all the way back to a mathematical papyrus roll from ancient Egypt. We will compute the number of squares and rectangles on a chessboard, and we will learn the legend of a wise man who used a chessboard and the power of geometric growth to fool a king into promising something that was impossible for any earthly king to fulfill. And in the process, we will learn the art of summation.
M4334: The Story of e in Splash Spring 2015 (Apr. 11  12, 2015)
Starting from the evolution of interest rates in the Greek, Roman and Christian worlds, students will learn how Euler’s number e emerged in the context of calculating compound interest. The relationship between natural logarithms and e will also be looked at.
M4338: The story of pi in Splash Spring 2015 (Apr. 11  12, 2015)
How was the ratio of the circumference and diameter of a circle understood in Egypt, Mesopotamia, India and China? Students will learn about the approximation of pi derived by Archimedes. Modern developments will include the examination of the infinite series of Leibnitz, Gregory and Madhava.
P3911: The Flat Earth in Splash Fall 2014 (Nov. 08  09, 2014)
There was a time when people across different cultures believed that the earth was more or less flat, not because they were stupid in any way, but because reasoning by common sense led them to it. Even many of the best philosophers in ancient Greece adhered to some version of a flat earth viewpoint. How did some of the philosophers (or 'scientists' of the time) begin to claim that the earth was spherical? What observations and arguments led them to it? In this course, we will imagine travelling back in time to the ancient world, two thousand years before the advent of modern science, and understand how educated people convinced themselves and the others that the earth was really spherical, without satellite pictures and the ability to circumnavigate the world. We will look at the arguments offered by the key philosophers and astronomers of the time, including Aristotle and Ptolemy. Along the way, we will also understand the phases of the moon, and how the ancients inferred that eclipses are caused by the alignment of the sun, moon and the earth.
Note: This is a history of science class, not a regular science class.
M3925: Great Mathematicians: Euclid in Splash Fall 2014 (Nov. 08  09, 2014)
"At the age of 11, I began Euclid, with my brother as tutor. This was one of the great events in my life, as dazzling as first love. I had not imagined there was anything so delicious in the world... From that moment until I was 38, mathematics was my chief interest and my chief source of happiness." This is how Bertrand Russell, one of the most famous 20th century mathematicians (and also a Nobel Laureate) described his childhood encounter with Euclid's Elements. It is reputed to be one of the most widely read texts in the Western tradition, next only to the Bible. It has influenced scientists like Albert Einstein, politicians and lawyers like Abraham Lincoln, philosophers and mathematicians like Rene Descartes, political philosophers like Thomas Hobbes and even the ethics of Spinoza.
After reviewing the state of mathematics prior to Euclid, and the importance of the Museum of Alexandria, where Euclid was the first professor of mathematics, we will look at the chief contribution of Euclid for which he has been so influential  the axiomatic method, and the way he employs it to construct all of Greek mathematics in the Elements. We will devote most of our attention to his twodimensional geometry, which has come to be known as 'Euclidean geometry'. The Elements also has portions on number theory, and we will look at an elegant proof of the fact that there are an infinite number of primes.
Note: Though not required, we would recommend that you also enroll for Great Mathematicians: Thales and Great Mathematicians: Pythagoras if you're enrolling for this course.
M3929: The Story of Numbers in Splash Fall 2014 (Nov. 08  09, 2014)
How did we come up with the modern number systems? What are the important characteristics of the modern numbers that make them different from prehistoric ideas about numbers? Join us for a fascinating tour of the modern number system beginning from the prehistoric tally counting to the modern decimal systems. We will look at Mesopotamian, Egyptian,Greek, Roman, Chinese, Indian, Arabic and Mayan number systems and the emergence of the current system that we use.
M3930: Interest Rates and the emergence of the number 'e' in Splash Fall 2014 (Nov. 08  09, 2014)
From student loans and mortgages to the financial system, we see the use of interest rates everywhere. Wonder how the idea of charging interest started in the ancient world? Beginning from Hammurabi's code, we trace the evolution of interest rates in Greek, Roman and Christian world. How is the mysterious number e connected to something as practical as interest rates? You will learn about all this in this "interest"ing class.
M3935: Great Mathematicians: Thales in Splash Fall 2014 (Nov. 08  09, 2014)
Living in a time when mathematics, science and philosophy were not separate disciplines, Thales of Miletus is reputed to be the earliest philosopher in the Western intellectual tradition. From creatively determining the distance of a ship from the seashore, to calculating the height of the Great Pyramid using a simple stick; from predicting a solar eclipse to arguing that water is the origin of everything; from being an absentminded stargazer who fell into a well, to being a practicalminded merchant who made a good profit, we will look at the limited and uncertain historical sources that we have about this earliest philosopher who is reputed to have introduced the notion of 'proof' in mathematics.
M3936: Great Mathematicians: Pythagoras in Splash Fall 2014 (Nov. 08  09, 2014)
We have all heard of the Pythagorean Theorem, named after the Greek philosopher Pythagoras. But the Pythagorean Theorem was not discovered by Pythagoras. And it would be more accurate to look at Pythagoras as the founder of a religious community than as a mathematician.
In this class, we will look at the life and times of Pythagoras, one of the most enigmatic figures in history. We will look at his travels, his struggle to find students, and his subsequent rise to fame as the divine founder of a secretive religious community, that embraced mathematics as a core part of its religion, along with music, reincarnation and abstention from meateating. We will look at the relationship between music and mathematics that Pythagoras supposedly uncovered, his creation myth in which everything arises from number, and his influence on the scientific revolution much later. We will see how the discovery of irrationals shattered the worldview of the Pythagoreans, and we'll look at a possible proof of the Pythagorean Theorem that Pythagoras (or one of his followers) might have originally come up with.
Note: Though not required, we would recommend that you also enroll for Great Mathematicians: Thales if you're taking this course.
M3692: A Gentle Introduction to Calculus in Splash! Spring 2014 (Apr. 12  13, 2014)
It is considered to be one of the greatest achievements of the human mind. But Calculus is also the greatest source of terror and anxiety for students. In this course, we will build your intuition for this important area of mathematics, preempting any reason to be fearful of it. We will go into a brief history of its development from precursors in ancient Greece and India, to the modern calculus developed by Newton and Leibnitz in the 17th century. Through problems involving simple geometric concepts that you will participate in solving, you will come away with an appreciation for the two ideas underlying all of calculus  integration and differentiation.
M3696: Games of Chance: An Introduction to Probability in Splash! Spring 2014 (Apr. 12  13, 2014)
Our lives are significantly influenced by random events  weather forecasts, stock market fluctuations, the traits we inherit from our parents, car accidents, how well you do in your exams, etc  these are all examples where chance plays a role. Nowhere is that role more prominent than in games of chance. In tossing a coin, or rolling dice, or flipping cards, we are blatantly playing games of chance. In fact, it was in the context of gambling that the basic ideas of probability were first invented. We will look at those basics: what is probability, and how do we assign a numerical value to the likelihood of an event when we have no idea what will happen? Believe it or not, even basic questions like these about probability are still a source of debate among mathematicians (and we will see why). But that also makes probability one of the most interesting topics to learn about in mathematics. So we invite you to join in  you will enjoy the experience (with a high probability).
M3697: The Art of Summation in Splash! Spring 2014 (Apr. 12  13, 2014)
Summing the numbers from 1 to 5 can be done quickly. Summing the numbers from 1 up to 100 would take more time. Or is there a quick way to do it? How about the general problem of summing the numbers from 1 to N? We will look at a few different ways to approach problems of this kind, including a trick Gauss used when he was supposedly nine years old! We will generalize the solution to compute the sum of an arithmetic series.
$$\textit{As I was going to Saint Ives,}$$
$$\textit{I met a man with seven wives.}$$
$$\textit{Each wife had seven sacks;}$$
$$\textit{every sack had seven cats;}$$
$$\textit{Every cat had seven kits;}$$
$$\textit{Kits, cats, sacks and wives,}$$
$$\textit{How many were going to Saint Ives?}$$
This children's rhyme will initiate us into summation of a different kind of series  a geometric series.
We will also play with other summations: summing the first n squares, or the first n cubes, and try to discover connections between these different series.
To sum up, it'll be fun, so come and join us!
M3698: Great Mathematicians Pythagoras in Splash! Spring 2014 (Apr. 12  13, 2014)
The first of the great Greek mathematicians, Pythagoras had a fascination for numbers and geometric shapes that raised their status to attributes of God! By studying his work, we will see the beginning of pure mathematics in Greece and contrast it with the more applied mathematics that was prevalent in ancient India and Egypt.
Any mention of Pythagoras is incomplete without his theorem, probably the most known mathematical theorem in the world. Do you know people have claimed over 350 proofs of the theorem? You will rediscover some of these proofs on your own in an interactive session.
M3699: Great MathematiciansEuclid in Splash! Spring 2014 (Apr. 12  13, 2014)
The first person in Greece to actually systematically publish mathematics books covering both arithmetic and geometry, Euclid was instrumental in bringing ideas of great Greek mathematicians together. Believe it or not Euclid’s book “the Elements” is the most printed book after the Bible in the western world. We will cover the basic principles of geometry he used to derive many results in planar geometry. And we will also discuss a fascinating method Euclid found to get the greatest common divisor of two numbers.
M3700: Great MathematiciansArchimedes in Splash! Spring 2014 (Apr. 12  13, 2014)
Considered one of the greatest mathematicians and physicists among the ancients, we will see Archimedes’s contribution specifically in computing areas and volumes of different shapes and his fascination with the number infinity. Want to know how the value of the famous number pi comes from? To appreciate Archimedes better, you will interactively learn his approximation to pi.
M3288: Permutations and Combinations in Splash! Fall 2013 (Nov. 02  03, 2013)
A brief introduction to the interesting topic of permutations and combinations. We will cover problems on fundamental principles of counting, permutations and combinations
M2941: Couting, Permutations and Combinations in Splash! Spring 2013 (Apr. 13  14, 2013)
Permutations and Combinations is an interesting topic that is also foundational to the study of Probability. Let us have fun and count ways to arrange objects into groups, arrange numbers, alphabets and poker cards.
M2518: The mystery of probability in Splash! Fall 2012 (Nov. 03  04, 2012)
From stock markets to quantum mechanics to weather to life decisions, probability impacts all areas of our life. This class will be giving the intuition behind foundations of probability theory and mix it with fun problem solving.
M2056: Lets Get to Solving Problems! in Splash! Spring 2012 (Apr. 21  22, 2012)
The course will describe the overall process of solving mathematical problems. The process consists of four phases:(1) Understanding the problem (2) Choosing a specific approach to solve the problem
(3) Examining the insights gained through that approach
(4) Repeat Steps 23 recursively to get closer to the solution.
Multiple illustrative examples will be picked to demonstrate the various heuristic approaches used to solve arithmetic puzzles, problems in geometry, algebra and probability.
The course will be loosely based on " How to Solve it: A New Aspect of Mathematical Method" by George Polya http://www.amazon.com/HowSolveMathematicalPrincetonScience/dp/069111966X, which is a highly recommended preliminary book for students aspiring to be good problem solvers.
