Summer camp -- Adventures in Mathematical Problem-Solving

When given a question to answer, many students think only for a few seconds to figure whether they can see a method to answer the question, and give up otherwise. They are habituated to being given "exercises", questions that test whether you can apply a known method for calculating the answer. But what is one to do when it's not at all clear what method to use? A "problem" is a question that one does not know (at the outset) how to solve, and which hence appears to be difficult. In contrast to exercises, solving problems requires a very different mindset. You need to take time to patiently explore an unknown terrain, get your hands dirty, investigate what happens if you turn left or turn right, come up with strategies to get to the desired 'destination' (the solution), and see where they lead you. You have to learn to cope with failure, to encounter dead ends, to get lost, and keep exploring. All this makes solving problems more difficult than solving exercises, but also more fun. Isn't hiking in an unknown terrain more fun than doing repetitive exercises in a gym? You can expect surprises, thrilling moments of discovery along with frustrating moments of feeling lost and confused. 

In this course aimed at middle school students, we will learn the art of solving problems in mathematics. It will not only prepare you for contests like the Math Olympiad and deepen your understanding of the school curriculum, but also provide you plenty of moments of thrill and discovery where you will learn to use effective strategies to find your own creative solutions to problems. The problems will be drawn from the history of mathematics, from games and puzzles, from math contests and from real world situations.  

Topics we will cover will include:

1. Problem Solving Strategies, along with plenty of examples of problems to hone each strategy. Some of the strategies we will cover are -- drawing pictures/diagrams, systematic enumeration of possibilities (in the form of lists, tables, trees and graphs), solving simpler instances of the problem, uncovering patterns, making reasonable guesses, experimenting with models, working backwards, writing equations, changing your point of view, looking at extreme values, exploiting parity and symmetry, pigeonhole principle, invariants, geometric transformations, mathematical induction, etc. 

2. The World of Mathematical Proofs and Logic: A proof is an argument that establishes the truth of a theorem using logic. We will look at different proof techniques to build creative mathematical arguments. Once you learn the art of proving claims, you will never be satisfied with just memorizing formulas. You will want to know WHY they're true. 

3. Special focus on some of the celebrity numbers (fibonacci numbers, prime numbers, i, pi, e), celebrity theorems (Pythagorean Theorem, etc), and celebrity people (Pythagoras, Euclid, Archimedes, Descartes, Newton, Fermat, Gauss, Euler, Riemann, etc) in mathematics.

Timings and Venue:

Our 8-week summer camp will be held from June 16, 2014 to August 15, 2014.

Classes will be held Mon-Fri from 9 am to noon. If there is enough demand, then we may have classes in the afternoon as well.

The classes will be held in Cupertino, on DeAnza Blvd (near McClellan/DeAnza).

Maximum class size will be 18 students. 

Instructors: 

Omkar Deshpande

Principal Engineer at WalmartLabs.
M.S & Ph.D, Computer Science, Stanford University
B.Tech, Computer Science and Engineering, IIT Delhi

Vivek Kaul 

Data Scientist at Facebook
M.S & Ph.D, Electrical and Computer Engineering, Georgia Tech
B.Tech, Aerospace Engineering, IIT Bombay

For more details, please look at the "About Us" page. 

Cost:

A half-day summer camp (9 am to noon) will cost 275$ a week. You need not enroll for the full 8 weeks, in which case you will only be charged for the number of weeks you are enrolled in. 

Contact Information and Registration Information:

If you have any questions about the program, please send us an email at omkar.vallabh@gmail.com. To register, please fill out this form, or alternatively, please send us the following information by email:
1. Full name of your child
2. Name of school he/she will attend in Fall 2014, and Grade Level
3. Parent's Email and Address (which will be used only for contacting you with information about our classes, and will not be shared with anyone outside)
4. Number of weeks you expect to enroll your child for (this can be tentative if your summer plans are not fully clear, but please mention the word "tentative" in that case)
5. Names of other math and science programs/classes your child is attending (or has attended) outside of school, in the last one year.

FAQ

1. What is "The Young Socratics"? 

The Young Socratics is an educational program in Math and Science geared towards middle school students, with an emphasis on problem-solving, and on understanding the relevant subjects (Math and Science) using the lens of history. 

We believe that all the different subjects (Math, Science, Social Studies, Literature, Art, etc) need to ideally be integrated together into a coherent and meaningful body of knowledge for the student, rather than being compartmentalized into different subjects with little or no connection to one another. For example, when studying about political, economic, social and religious life in ancient Mesopotamia in history classrooms, the students should also be exposed to the mathematics and astronomy of the Babylonians. This should in fact be the primary way by which to introduce mathematical and scientific ideas. They should learn about the creative development of mathematical and scientific ideas in their historical context, rather than directly being told about their final forms in the present. They need to experience the intellectual journey of humans by encountering these ideas in the chronological manner in which they developed. They should experience the confusion, the frustration, the suspense, and the thrills of that human journey. This narrative ("story") approach is bound to motivate students more, and lead to a better understanding of those ideas. 

Along with a historical viewpoint, children should also be given problems to solve that would require them to think and discover what approaches might lead to the solution or answer. These problems can be of 4 types. 

a) Historical problems: These problems are meant to make the students think about certain questions like past mathematicians or scientists might have thought about them. Here is an example -- "If you were living in ancient Egypt or ancient Greece, without the tools and theories of modern science, would you have believed the earth was curved, or would you have believed it was flat? What reasons would you have offered in support of your beliefs?" The arguments offered by students can be explicitly 'matched' with the arguments of the ancient Greeks in support of a curved earth, given in the writings of Aristotle or Ptolemy. Once they understand (or who knows, perhaps even independently come up with) the reasons why the ancient Greeks believed the earth was curved approximately like a sphere, they can then be given a new problem -- how would you compute the size of the earth? Such problems would provide the right context for introducing ideas from geometry, trigonometry and astronomy. 

b) Problems on puzzles and games. Since children enjoy games and puzzles, such problems can also be a good launchpad for developing an interest in mathematical topics. For example, card games, roulette, Tic Tac Toe, Soduku, Chess, Rubik's Cube etc can all be used for introducing ideas from probability, permutations and combinations, and other topics from discrete mathematics. 

c).Problems illustrating aesthetic beauty: These are problems where some of the solutions have elegance and beauty to them (e.g, certain proofs of the Pythagorean Theorem, or Euclid's proof that there are infinitely many prime numbers), or problems which have the potential to reveal unexpected connections between different areas of mathematics (e.g, number theory and geometry, or algebra and geometry)

d) Problems illustrating applications to technology: These could be applications of math or science to the development of technology (e.g, after learning about transistors and logic gates, can you build an adder?), or measurement of some quantity (e.g, computing the height of a lighthouse or the width of a river). 

2. What does the name "The Young Socratics" signify?

Our approach to teaching the young minds enrolled in our program is to lead them step by step to new ideas by asking them appropriate questions (formulated as problems), and giving them some time to take those 'discovery' steps themselves as they try to grapple with those questions. We would like to evoke answers from within them, rather than directly laying down before them all the steps to the final solution. We also believe in encouraging students to ask questions for which we may not have the answers (and even open-ended questions for which even the best scholars may not have agreed-upon answers). They should learn to think critically, argue with themselves over these questions, and to argue with others. This scrutinizing approach to our subjects that we aim to teach our students resembles the Socratic method (used by the ancient Greek philosopher Socrates), hence the name. 

3. Will my child improve her grades in her subjects?

We believe that improvements in grades or scores in competitions should naturally follow as a good "side effect" of our program. Our main aim (however) is to cultivate in the student a strong desire and hunger to keep learning, and to derive great pleasure in that learning. 

4. Who are your instructors and what is their background? 

Please see http://theyoungsocratics.blogspot.com/2014/03/about-us.html

5. Will you be offering classes outside of summer? 

Yes, we're planning to have after-school classes and weekend classes after summer (and there is a possibility of starting before the summer as well if there is sufficient interest). Please email us at omkar.vallabh@gmail.com if you are interested in attending/shaping those classes. The curriculum is still being planned and developed, and if a sufficient number of people express interest in any particular subject or topic, we would be happy to tailor our classes to meet those needs. We do plan to align ourselves with the school curriculum, although we will cover the material in a different way, blending math and science with social studies and literature. 

6. What are the hourly charges for the classes? 

Our hourly charges for the summer classes are less than 20$ an hour. Along with the face to face classes, we will also have online videos made available for free to students who enroll in our classes, so the charges also include access to the online videos. These online videos will supplement the classroom program. The online videos will cover all the material being covered in the classroom, and also cover some extra material and problems. For a sample of what those problem videos might look like, please see https://www.youtube.com/playlist?list=PLakRmmd52BX4hvn-ccFLdfHKI9pGbPomA for worked out solutions to some MOEMS problems.
If students have doubts that can't be answered due to time constraints in the classroom, we will try to answer them by making videos. That will be another purpose of the videos. 

About us

Omkar Deshpande

Omkar started The Young Socratics to try a different approach to teaching the regular middle and high school curriculum, which would not be compartmentalized, feel burdensome or boring, or devoid of joy and meaning. During the six years he spent at Stanford University towards his MS and Ph.D in computer science, he also attended classes and talks by professors in widely different disciplines (especially the humanities), and did interdisciplinary research spanning computer science, genetics and cultural anthropology. He came to believe that discipline boundaries, though convenient for specialists, prevent one from appreciating the interconnected nature of all human knowledge. He firmly believes in blending the teaching of math and science with the humanities (with a special emphasis on history and philosophy), without sacrificing the development of practical problem-solving skills. He earned his BS in Computer Science from the Indian Institute of Technology, Delhi, and is currently working as a Principal Engineer at WalmartLabs (formerly Kosmix). 

Vivek Kaul

After working extensively in academic and industrial settings across multiple disciplines, Vivek decided to join The Young Socratics and work on the vision of providing fundamental science and mathematics education integrated with their historical and philosophical context.  According to him, education consists of laying out a series of paths for the students to discover and create new pathways on their own.  Sadly such educational exposure is hardly provided to most students before graduate school and by that time many lose their interest.  Therefore, he believes that the foundation for such education should be laid pretty early and that motivated him to work with middle school and high school students. Vivek has M.S degrees in Aerospace Engineering, Computer Engineering and Mathematics respectively and a PhD degree in Electrical and Computer Engineering from Georgia Tech. He obtained his B.S  in Aerospace Engineering from Indian Institute of Technology Bombay and is currently working as a Data Scientist at Facebook.