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education_en.html
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<!doctype html>
<html>
<head>
<meta name="viewport" content="width=device-width,initial-scale=1" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Junao Yu's Homepage</title>
<link href="style.css" rel="stylesheet" type="text/css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.12.0/katex.min.css" integrity="sha384-fhYLJZkbU8EZ0R6AxN8I6YTILgGrhYZVXZ2j24MVKSTOvqtCPcd6yAevPl+4TuRW" crossorigin="anonymous">
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</head>
<body bgcolor="#FFFAF0" lang=CN-CN link=blue vlink=blue style='tab-interval: .5in'>
<body>
<div id="title" align="center"><strong class="title" style="color:black">Junao Yu's Homepage</strong>
<table width="800" border="0">
<tr>
<td style="border: 0px" width="168" class="table"><div align="center"><a href="index_en.html">Personal Introduction</a></div></td>
<td style="border: 0px" width="168" height="31" class="table"><div align="center"><strong>Education</strong></div></td>
<td style="border: 0px" width="168" class="table"><div align="center"><a href="life_en.html">Campus Life</a></div></td>
<td style="border: 0px" class="table"><div align="center"><a href="education.html">中文版</a></div></td>
</tr>
</table>
</div>
<hr>
<div style="border: 0px solid #000000; width: 1000px; margin: 0 auto;">
<div align="left">
<h1>Core Courses:</h1>
<table width="900" border="1" align="center">
<tr><td style="border: 1px" class="text" valign="top" align="left">
<!--<strong class="table">Core Courses</strong>
<table frame="border" rules="all" align="center">-->
<tr>
<th> Course </th>
<th> Credit </th>
<th width="300"> Instructor</th>
<th> Grade </th>
</tr>
<tr>
<td>  Foundations of Geometry   </td>
<td>   3   </td>
<td>   Mao Sheng   </td>
<td>   96   </td>
</tr>
<tr>
<td>  Foundations of Algebra   </td>
<td>   3   </td>
<td>   Liming Ma   </td>
<td>   87   </td>
</tr>
<tr>
<td>  Mathematical Analysis(A1)   </td>
<td>   6   </td>
<td>   Guangbing Ren   </td>
<td>   88   </td>
</tr>
<tr>
<td>  Mathematical Analysis(A2)   </td>
<td>   6   </td>
<td>   Jiansong Deng   </td>
<td>   89   </td>
</tr>
<tr>
<td>  Mathematical Analysis(A3)   </td>
<td>   4   </td>
<td>   Dafeng Zuo   </td>
<td>   96   </td>
</tr>
<tr>
<td>  Linear Algebra(A1)   </td>
<td>   5   </td>
<td>   Xinmao Wang   </td>
<td>   97   </td>
</tr>
<tr>
<td>  Linear Algebra(A2)   </td>
<td>   4   </td>
<td>   Xinmao Wang   </td>
<td>   90   </td>
</tr>
<tr>
<td>  Introduction to Differential Equations   </td>
<td>   3   </td>
<td>   Lifeng Zhao   </td>
<td>   88   </td>
</tr>
<tr>
<td>  Real Analysis (H)   </td>
<td>   4   </td>
<td>   Guangbin Ren   </td>
<td>   95   </td>
</tr>
<tr>
<td>  Complex Analysis (H)   </td>
<td>   4   </td>
<td>   Haozhao Li   </td>
<td>   79   </td>
</tr>
<tr>
<td>  Modern Algebra   </td>
<td>   3   </td>
<td>   Lei Zhang   </td>
<td>   86   </td>
</tr>
<tr>
<td>  Probability Theory   </td>
<td>   3   </td>
<td>   Dangzheng Liu   </td>
<td>   83   </td>
</tr>
<tr>
<td>  Probability Theory-Outer Chapter   </td>
<td>   1   </td>
<td>   Dangzheng Liu   </td>
<td>   90   </td>
</tr>
<tr>
<td>  Functional Analysis   </td>
<td>   3   </td>
<td>   Congwen Liu   </td>
<td>   83   </td>
</tr>
<tr>
<td>  Advanced Real Analysis*   </td>
<td>   4   </td>
<td>   Jungang Li   </td>
<td>   96   </td>
</tr>
<tr>
<td>  Topology (H)   </td>
<td>   4   </td>
<td>   Gao Chen   </td>
<td>   90   </td>
</tr>
<tr>
<td>  Differential Geometry (H)   </td>
<td>   4   </td>
<td>   Shiping Liu   </td>
<td>   75   </td>
</tr>
<tr>
<td>  Harmonic Analysis*   </td>
<td>   4   </td>
<td>   Jingwei Guo   </td>
<td>   82   </td>
</tr>
<tr>
<td>  Introduction to Ergodic Theory*   </td>
<td>   4   </td>
<td>   Song Shao   </td>
<td>   90   </td>
</tr>
<tr>
<td>  Topics in Analysis*   </td>
<td>   4   </td>
<td>   Jungang Li   </td>
<td>   100   </td>
</tr>
<tr>
<td>  Modern Partial Differential Equations*   </td>
<td>   4   </td>
<td>   Xi-nan Ma   </td>
<td>   96   </td>
</tr>
<tr>
<td>  L.-K. Hua's Seminar(H)   </td>
<td>   4   </td>
<td>   Yong Wei   </td>
<td>   97   </td>
</tr>
</table>
Note: (H) represents the curriculum of honors; * represents graduate courses.
</div>
<!--
<h2>Currently Learning: </h2>
<p>Differential Manifolds, Algebraic Topology, Nonlinear Elliptic Equations, Combanitics.</p>
-->
<td colspan="1" valign="top" class="text" style="border: 0px" width="800" align="left"><hr>
<h1>Research details:</h1>
<h2>Undergraduate Innovation Plans, Advisor：Prof. Congwen Liu</h2>
<i>On Beckner's Inequality for Axially Symmetric Functions on S^n. </i>
<p>
Introduction:
The conjecture of Beckner's inequality is a higher dimensional extension of Nirenberg problem in conformal geometry.
In recent years, Prof. Changfeng Gui and Juncheng Wei have made a breakthrough when the dimension n=4,6,8 together with their groups.
In this program, we aim to study their works, simplify the proof, and hopefully solve the problem in higher dimensions.
</p>
<h2>L.-K. Hua Seminar (H), Advisor：Prof. Yong Wei.</h2>
<h2>Advanced Functional Analysis Seminar.</h2>
<p>Reference: Michael Reed, Barry Simon. <i>Methods of Mathematical Physics-Volume 2</i></p>
<p>
Introduction:
Functional analysis acts as a significant role in PDE, geometry analysis, mathematical physics and varieties of other subjects.
In this seminar, we focus on advanced theories such as semigroup of operators and spectrum of unbounded operators.
With more profound comprehension in functional analysis and its applications, we are going to discuss some frontier problems.
</p>
<h2>Summer Research Internship at Purdue University, Advisor：Prof. Changyou Wang.</h2>
<i>Nonlinear Fluid Equations and Harmonic Maps. </i>
<hr>
<h1>Electronic Notes:</h1>
<p> <a href="MyFiles/MagnetismFormulas.pdf">Formulas in Magnetism</a>, 2022 Fall.</p>
<p> <a href="MyFiles/ClassicalPDEs.pdf">Classical PDEs</a>, 2022 Fall.</p>
<p> <a href="MyFiles/CA.pdf">Complex Analysis</a> , 2023 Spring.</p>
<p> <a href="MyFiles/Optics.pdf">Optics</a>, 2023 Spring.</p>
<p> <a href="MyFiles/AtomicPhysics.pdf">Atomic Physics</a>, 2023 Spring.</p>
<hr>
<h1>Other Resources: </h1>
<p> <a href="MyFiles/数学分析讲义第一册解答.pdf">Complete Solution to Mathemical Analysis (B1)</a>.</p>
<p> <a href="MyFiles/24SpringHA.pdf">Solutions to Exercises of the Graduate Course Harmonic Analysis</a>.</p>
<p> Lecture Notes for exercise class of Mathemical Analysis (B1):<a href="MyFiles/2.pdf">2</a>,<a href="MyFiles/6.pdf">6</a>,<a href="MyFiles/9.pdf">9</a>.</p>
<p> <a href="MyFiles/交响乐赏析.pdf">Assignment of Symphony Admiration</a> (Topic: Revolution and Romance).</p>
<p> <a href="MyFiles/艺术的启示.pdf">Assignment of Inspiration of Arts</a>.</p>
<p> <a href="MyFiles/HofU_Assignment.pdf">Assignment of Habitability of the Universe</a>.</p>
</tr>
</table>
</div>
<hr>
<div align="center"> Latest Modification : 08/10/2024</div>
</body>
</html>