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<!DOCTYPE html>
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<li>
<a class="page-scroll" href="#undergraduate">Undergraduate Notes</a>
</li>
<li>
<a class="page-scroll" href="#graduate">Graduate Notes</a>
</li>
<li>
<a class="page-scroll" href="#teaching">Teaching</a>
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<section id="intro" class="extra-section">
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<div class="row" id="undergraduate">
<div class="col-lg-12">
<p>This page is a collection of notes that I wrote in my undergraduate and graduate studies. Due to a Google Drive privacy update, some of the links may be broken; in this case, request permission to access the file and I will update the link. If you would like the source code for my notes, <a href="/latex">click here</a>.</p>
</div>
<div class="row">
<div class="col-lg-12">
<h1>Undergraduate Notes</h1>
<p>Here is a collection of notes that I have written as an undergraduate at UC Berkeley. I also contributed to the course notes for EECS 126 in Spring 2018 and prepared slides and notes for COMPSCI 70 in Summer 2018, which can be found on the respective course websites: <a href="https://inst.eecs.berkeley.edu/~ee126/sp18/">here</a> and <a href="http://www.su18.eecs70.org/">here</a>. Finally, <a href="/extra">here</a> is a collection of other miscellaneous notes and pieces.</p>
<div class="col-lg-4">
<h3>COMPSCI 70</h3>
<h5>Discrete Mathematics & Probability Theory</h5>
<ul>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5N1VSUGRyTC1RS28/view?usp=sharing&resourcekey=0-usGJvlG9TWbjzUJFUmJCxQ">Midterm 1 Review Slides (Fall 2016)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5cXFacVZwQlZpM3c/view?usp=sharing&resourcekey=0-2tmp1EbCaVfH4qFx_qlgFQ">Continuous Probability Review Slides (Fall 2016)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5Wnh5M2VEa05DNWs/view?usp=sharing&resourcekey=0-OaXGlNeneSp79WNshWYh5A">Tips & Tricks in Probability Slides (Fall 2016)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5c3BvX3hvSlktdzA/view?usp=sharing&resourcekey=0-vjc6tfu02vKSYUAje2Fozg">Final Review Slides (Fall 2016)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5YWoxYmQ2RjdTdGc/view?usp=sharing&resourcekey=0-jWSXI7uAK6xGsmBXBmErrA">Markov Chains & Continuous Probability Slides (Spring 2017)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5Z3dSN1FTSnNLaFk/view?usp=sharing&resourcekey=0-9GqDW5QDwWrfYPfDFvuxVQ">Extra Note 1: Cauchy Induction</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5Ukp0Y00xbjgtRlU/view?usp=sharing&resourcekey=0-wAM2EIt5O4u2mTWkw65qPg">Extra Note 2: Top Trading Cycles (TTC) Algorithm</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5cjh2S0pNc2VHV00/view?usp=sharing&resourcekey=0-NQufShXwQTrDz_M5e1txXg">Extra Note 3: Chinese Remainder Theorem</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5bXRQdDF6NGN3WWs/view?usp=sharing&resourcekey=0-bctnbZBC1Tk_WYrD5wN8HA">Extra Note 4: Hard Problems & Public Key Cryptosystems</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5RFdFUXpsSFdVRnM/view?usp=sharing&resourcekey=0-KHtbccNknYUMedxsfusd5Q">Extra Note 5: Eisenstein's Criterion</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5dHRzYWR3SXhYa0k/view?usp=sharing&resourcekey=0-zUJ-lovAiEZh5ps_-iVxIA">Extra Note 6: Algebraic Coding Theory</a>
</li>
<li>
<a href="https://drive.google.com/open?id=0B_WFOD8f4jS5YklsNnZlWUExODg">Extra Note 7: Cantor-Schröder-Bernstein Theorem</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5ekVWejhDeHdnSXM/view?usp=sharing&resourcekey=0-N2-WPaKv7kcRNIeZGN77VQ">Extra Note 8: Generating Functions</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5NEhMQ3NSMXJwUXc/view?usp=sharing&resourcekey=0-Dkh9E6KcQneRy0-izpl6Yw">Extra Note 9: Generating Functions II</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5NC1oZ2lRSWZFZzA/view?usp=sharing&resourcekey=0-3N1CHvK1slXtklOf-beuzw">Extra Note 10: Pairwise Independent Hash Functions</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5X3pLYjZNMzZhU1k/view?usp=sharing&resourcekey=0-p4jqT6kWn1HUflpOk_nbDg">Extra Note 11: Moment-Generating Functions</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5c1BNZFhxLW5GRWs/view?usp=sharing&resourcekey=0-dJvY2VRhwVMfO9EeLbiwLw">Extra Note 12: Jensen's Inequality</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5YjUyaVdJRG9UT0E/view?usp=sharing&resourcekey=0-mLKIf0NojFUCVrnZ6qmYOw">Extra Note 13: Martingales</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5R0dZamVmbXlweEk/view?usp=sharing&resourcekey=0-_qkF8HEZDrYvzvkXbI0TpQ">Extra Note 14: PageRank</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5dkl1SGVqOEJ6bk0/view?usp=sharing&resourcekey=0-6RiKFt2oaI58AKxVXylG7g">Extra Note 15: Beta Distribution</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5aFU1ZGowVlk4Nmc/view?usp=sharing&resourcekey=0-QZyVbZJ9VvrYyPjff2tqEA">Propositional Logic: Quantifier Distribution Problem</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5MjB2MnhvT1hEOFk/view?usp=sharing&resourcekey=0-OdR86qPw1xTFv0RWstJfhg">Induction: Celebrity Algorithm Problem</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5VmNHeEtkVGk1d00/view?usp=sharing&resourcekey=0-KNxc7oMyjsoEWpXEOYMNNg">Continuous Probability: Continuous Conditional Expectation Problem</a>
</li>
</ul>
</div>
<div class="col-lg-4">
<h3>OTHER CLASSES</h3>
<h5></h5>
<ul>
<li>
<a href="https://drive.google.com/open?id=1Jg9vWH196rzGhqDuXXvvkafRGQgjCcMz">COMPSCI 271 (Randomness & Computation)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=18sIiNqCplECywr2sbkZBVd21ySCj1zph">EL ENG 223 (Stochastic Systems: Estimation & Control)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1PXsncv39CHloXiB126i0MbYPQWwPAieB">EL ENG 226A (Random Processes in Systems)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5ejAyTm9nZGFzRzQ/view?usp=sharing&resourcekey=0-v_Xirnl5Cfq5FEGQTCCFQQ">MATH 115 (Introduction to Number Theory)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5NDdqSnJtM004Y2c/view?usp=sharing&resourcekey=0-122ZGTyytqwmYZ129q1W0A">MATH 135 (Introduction to the Theory of Sets)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1qxHn16pP0u2MHUhD39dO_e9hcr7Nz6Su">MATH 141 (Elementary Differential Topology)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5VThqYURRYU5mZUU/view?usp=sharing&resourcekey=0-3oUuz6tkqmjb9wlWoGYx3g">MATH 185 (Introduction to Complex Analysis)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5SnU2ZFoydVJUXzA/view?usp=sharing&resourcekey=0-SJ_IG0UtZ0Jazh0K1VqyFw">MATH C218A/STAT C205A (Probability Theory)</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5MUJ3M3g1SnowOTg/view?usp=sharing&resourcekey=0-WWnF4AWwURWOexmfjo2gYg">MATH C218B/STAT C205B (Probability Theory)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1Z6bHDkDuvK5_EGLG1b7WnIyEMv0corFp">STAT 210A (Theoretical Statistics)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=19xCJElPd58xitn9UV9mBmiORDkQ2oa-K">STAT 210B (Theoretical Statistics)</a>
</li>
</ul>
</div>
<div class="col-lg-4">
<h3>PROBABILITY NOTES</h3>
<h5></h5>
<ul>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5VGVhcFpSdGFKeUk/view?usp=sharing&resourcekey=0-K6gpJvvRp7hnDHT6m5sBbQ">0: Combinatorics</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5TkFOYS1xLUQxSVE/view?usp=sharing&resourcekey=0-S4Mi9adK4842nCUFgJZfTQ">1: Probability Theory</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5a3lmX1BPSEVDZ2c/view?usp=sharing&resourcekey=0--8qtC_Vuq4UJ_7JIrdM3YA">2: Discrete Random Variables</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5Y0hfRm9KcmJyVVk/view?usp=sharing&resourcekey=0-0jnLd-5JWF0GcxIsgSlOig">3: Variance & Inequalities</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5aG9NZVNVTGJrUzQ/view?usp=sharing&resourcekey=0-nM7B30IGUT7_4v3IYH3ARA">4: Regression & Conditional Expectation</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5aHRlVUxGVEZGVXM/view?usp=sharing&resourcekey=0-0-KvxQDIzOXjW05wA_Ot3w">5: Markov Chains</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5UnJwWjI0VlZNSzg/view?usp=sharing&resourcekey=0-8sVonhA8wGasI0XLAT10gg">6: Continuous Probability I</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5anZZSGhrNTEycGM/view?usp=sharing&resourcekey=0-bsRH6SkTicfW_zj94tE4Bw">7: Continuous Probability II</a>
</li>
<li>
<a href="https://drive.google.com/file/d/0B_WFOD8f4jS5QWdiSk5XLV9ITEk/view?usp=sharing&resourcekey=0-6V_PVPb5x5cOEyaivbmBhw">8: Information Theory</a>
</li>
</ul>
</div>
<div class="clearfix visible-lg-block">
</div>
</div>
<div class="row">
<div class="col-lg-12" id="graduate">
<h1>Graduate Notes</h1>
<p>Here is a collection of notes that I have written as a PhD student at MIT.</p>
<div class="col-lg-4">
<h3>CLASS NOTES</h3>
<h5></h5>
<ul>
<li>
<a href="https://drive.google.com/open?id=1n6Vc5uq694cJBfpm9QIbaVhRvltedcHU">18.137 (Topics in Geometric PDEs)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1zCswDvMCPYD7btkPXMwgz_X90uWAl2zq">18.1521 (Introduction to Partial Differential Equations)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1plWkWjEK7NTodBUyyzesflzjTwLlD3De">18.158 (Topics in Differential Equations)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1mcsB4oLMRNKXcloeVpl7jVlvB3xLk_i3">18.176 (Stochastic Calculus)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1UCuRTK2M5vmJkjAecBYFwil6BW0JbdoD">18.338 (Eigenvalues of Random Matrices)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1xeZHlFC8xoM4lc-1bJgQwQfNg-bfSMol">18.966 (Geometry of Manifolds II)</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1NjWUfhNyI2dLD6lBjwIB2a18C4B6YFf_">COMPSCI 229R (Topics in Theoretical Computer Science: Interactions between Physics and Computation)</a>
</li>
</ul>
</div>
<div class="col-lg-4">
<h3>OTHER NOTES</h3>
<h5></h5>
<ul>
<li>
<a href="https://drive.google.com/open?id=10xreIn13pS_SlZfEUb2GQVE2jhk-1piy">18.177 Presentation: Non-Linear Large Deviations via Gaussian Gradient Width</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1W1m6ZwdnUT2YyTCm5AHwDCGxX6cPz4Fz">18.338 Presentation: Sparse PCA</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1qx70TeV2khqKKYYUhCrzp59B5J_7a34M">COMPSCI 229R Official Scribe Notes</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1eIn1uPo2e0is5PWS-yjyeshJtgs7lgK8">Estimating Functionals of Discrete Distributions</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1mxO7OT_haZ9uO68PaXj1TVcTkHp_hScz">Metric Geometry for Statistics</a>
</li>
<li>
<a href="https://drive.google.com/open?id=1CItYUSQ7vhPL4p3gl-7Ic3JKqp-oPpQU">TAP Free Energy</a>
</li>
</ul>
</div>
</div>
</div>
<div class="row">
<div class="col-lg-12" id="teaching">
<h1>Teaching</h1>
<p>Here is a list of courses that I have taught in the past.</p>
<br>
</div>
<div class="row">
<div class="col-lg-6">
<ul>
<i>Summer 2018</i><br>
<div>
<b>
<a href="https://www.su18.eecs70.org/">Computer Science 70</a>
</b> – Discrete Mathematics & Probability Theory [co-taught with Vrettos Moulos]
</div>
</ul>
</div>
</div>
<div class="col-lg-12">
<p>I have also been a TA for these courses.</p>
<br>
</div>
<div class="row">
<div class="col-lg-6">
<ul>
<i>Spring 2016</i><br>
<div>
<b>
<a href="http://inst.eecs.berkeley.edu/~cs70/sp16/">Computer Science 70</a>
</b> – Discrete Mathematics & Probability Theory (Satish Rao, Jean Walrand)
</div>
</ul>
</div>
<div class="col-lg-6">
<ul>
<i>Fall 2016</i><br>
<div>
<b>
<a href="http://fa16.eecs70.org/">Computer Science 70</a>
</b> – Discrete Mathematics & Probability Theory (Sanjit Seshia, Jean Walrand)
</div>
</ul>
</div>
</div>
<div class="row">
<div class="col-lg-6">
<ul>
<i>Spring 2017</i><br>
<div>
<b>
<a href="http://sp17.eecs70.org/">Computer Science 70</a>
</b> – Discrete Mathematics & Probability Theory (Satish Rao)
</div>
<div>
<b>
<a href="http://inst.eecs.berkeley.edu/~ee126/sp17/">Electrical Engineering 126</a>
</b> – Probability & Random Processes (Kannan Ramchandran)
</div>
</ul>
</div>
<div class="col-lg-6">
<ul>
<i>Summer 2017</i><br>
<div>
<b>
<a href="http://www.su17.eecs70.org/">Computer Science 70</a>
</b> – Discrete Mathematics & Probability Theory (Hongling Lu, Vrettos Moulos, Allen Tang)
</div>
</ul>
</div>
</div>
<div class="row">
<div class="col-lg-6">
<ul>
<i>Fall 2017</i><br>
<div>
<b>
<a href="http://www.fa17.eecs70.org/">Computer Science 70</a>
</b> – Discrete Mathematics & Probability Theory (Kannan Ramchandran, Satish Rao)
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<b>
<a href="http://inst.eecs.berkeley.edu/~ee126/fa17/">Electrical Engineering 126</a>
</b> – Probability & Random Processes (Abhay Parekh, Jean Walrand)
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<i>Spring 2018</i><br>
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<b>
<a href="https://inst.eecs.berkeley.edu/~ee126/sp18/">Electrical Engineering 126</a>
</b> – Probability & Random Processes (Kannan Ramchandran)
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<p>I have led some Directed Reading Programs (DRP): <a href="/drp-2019">2019</a>, <a href="/drp-2020">2020</a>, <a href="/drp-2021-ml">2021(A)</a>, <a href="/drp-2021-stat">2021(B)</a>. I also taught a mini-course on log-concave sampling as part of a workshop on the <a href="http://www.crm.sns.it/event/506/timetable.html#title">Mathematics of Machine Learning</a> at the Centro De Giorgi; the first video can be found <a href="https://www.youtube.com/watch?v=bsIPm4jEXPA">here</a>.</p>
<p>In 2016-2017, I won the <a href="https://www2.eecs.berkeley.edu/Students/Awards/13/">EECS Outstanding GSI/Distinguished GSI Award</a>.
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