-
Notifications
You must be signed in to change notification settings - Fork 1
Expand file tree
/
Copy pathexposition.html
More file actions
170 lines (146 loc) · 9.12 KB
/
Copy pathexposition.html
File metadata and controls
170 lines (146 loc) · 9.12 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
<!doctype html>
<html class="no-js" lang="">
<head>
<meta charset="utf-8">
<meta http-equiv="x-ua-compatible" content="ie=edge">
<title>Mathematics Undergraduate Student Association</title>
<meta name="description" content="">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<link rel="manifest" href="site.webmanifest">
<link rel="apple-touch-icon" href="icon.png">
<!-- Place favicon.ico in the root directory -->
<link rel="stylesheet" href="css/normalize.css">
<link rel="stylesheet" href="css/main.css">
<link rel="stylesheet" href="css/musa.css">
<link rel="stylesheet" href="css/Dropdown.css">
</head>
<body>
<!--[if lte IE 9]>
<p class="browserupgrade">You are using an <strong>outdated</strong> browser. Please <a href="https://browsehappy.com/">upgrade your browser</a> to improve your experience and security.</p>
<![endif]-->
<!-- Add your site or application content here -->
<script src="js/vendor/modernizr-3.6.0.min.js"></script>
<script src="https://code.jquery.com/jquery-3.3.1.min.js" integrity="sha256-FgpCb/KJQlLNfOu91ta32o/NMZxltwRo8QtmkMRdAu8=" crossorigin="anonymous"></script>
<script src="https://d3js.org/d3.v6.js"></script>
<script src="https://unpkg.com/d3-dag@0.2.3/dist/d3-dag.min.js"></script>
<script>window.jQuery || document.write('<script src="js/vendor/jquery-3.3.1.min.js"><\/script>')</script>
<script src="js/plugins.js"></script>
<script src="js/Dropdown.js"></script>
<!-- <iframe src="sidebar.html" id="nav"></iframe>-->
<ul class="dropdown" id="nav">
<li><a href="index.html">About</a>
<ul>
<li><a href="friends.html">Friends</a></li>
<li><a href="office.html">Office Hours</a></li>
<li><a href="officers.html">Officers</a></li>
</ul>
</li>
<li><a href="academic.html">Academic</a>
<ul>
<li><a href="monday.html">Math Mondays</a></li>
<li><a href="ncumc.html">Conferences</a></li>
<li><a href="teaching_award.html">Teaching Award</a></li>
<li><a href="exposition.html">Exposition</a></li>
</ul>
</li>
<li><a href="outreach.html">Outreach</a>
<ul>
<li><a href="bump.html">BUMP</a></li>
</ul>
</li>
<li><a href="diversity.html">Diversity</a>
<ul>
<li><a href="sperry.html">Sperry Lecture</a></li>
</ul>
</li>
<li><a href="social.html">Social</a></li>
<li><a href="professional.html">Sponsor Us!</a></li>
</ul>
<div id="container">
<!-- About Section -->
<section id="exposition">
<h1>Exposition and Course Help</h1>
<img src="img/academic.jpg" style="display:block; margin-left:auto; margin-right:auto; width:300px">
<h3>Course Notes</h3>
<p>MUSA maintains course notes for use by their undergraduates.
The goal is to create easy-to-read summaries of core undergraduate courses, complete with examples
and practice problems.</p>
<p>If you'd like to see notes for a course you're taking or have taken, contact us at
musa@math.berkeley.edu or message us on Facebook!</p>
<p><ul>
<li><a href="resources/math185.pdf">Math 185</a>: Complex Analysis</li>
</ul>
<h3>Interactive Course Map</h3>
<!-- <p>Coming soon: hover over a course to see a brief description!</p> -->
<p>Hover over a course to highlight the prerequisites. Dashed lines indicate recommended prerequisites while solid lines indicate official prerequisites.<br>Designed and implemented by Andrew DeLapo.</p>
<script src="https://d3js.org/d3.v6.min.js"></script>
<svg id="coursemap" width=1200 height=1000 alt="interactive SVG element"></svg>
<script src="js/coursemap.js"></script>
<button id="toggle-grads" onClick="toggleGradClasses();">Show Grad Classes</button>
<h3>Undergraduate Course Map</h3>
<p>Black arrows indicate the lower-division courses, and other colors are for upper-division courses. These include official prerequisites as well as recommended ones.<br>Made by Sylvia Jin.</p>
<img src="course_map_info/coursemapv1.png" alt='Static Undergraduate Course Map' class='banner'>
<h3>Graduate Course Map</h3>
<p>Generously provided by u/Devilnaht on <a href="https://www.reddit.com/r/berkeley/comments/bm0w8o/berkeley_math_dependency_chart/">Reddit</a></p>
<p>Disclaimer: these only include official prerequisites. Different professors may vary the content semester to semester and thus have different requirements.</p>
<img src="https://i.redd.it/5i1wf8c1uww21.jpg" alt='Graduate Course map, credit to u/Devilnaht' class='banner'>
<h3>Exam Banks</h3>
<p>
<ul>
<li><a href="http://math.berkeley.edu/courses/archives/exams" target="_blank">Department's Exam Archive</a></li>
<li><a href="https://tbp.berkeley.edu/students/exams/math/" target="_blank">Tau Beta Pi's Exam Archive</a></li>
<li><a href="http://math.ucsd.edu/~pfitz/pastputnam.html" target="_blank">Putnam Exam Archive</a></li>
</ul></p>
<h3>LaTeX Tutorials</h3>
<p>LaTeX is a typesetting software which is commonly used in technical writing, including
formatting mathematics. MUSA holds a LaTeX workshop (Fall 2020 slides <a href="resources/LaTeX_Workshop.pdf">here</a>) once per semester, but if you missed it or
need more information, give these guides a try:</p>
<ul> <li><a href="http://artofproblemsolving.com/wiki/index.php/LaTeX:About"
target="_blank">Art of Problem Solving's Guide to LaTeX</a></li>
<li><a href="https://en.wikibooks.org/wiki/LaTeX/Mathematics" target="_blank">LaTeX: Mathematics on Wikibooks</a></li>
<li><a href="http://legacy-www.math.harvard.edu/texman/" target="_blank">Harvard Math Department's TeX Intro</a></li>
<li><a href="http://www.jmilne.org/not/CDGuide.html" target="_blank">Guide to Commutative Diagram Packages</a></li>
</ul></p>
<h3>Featured Problems</h3>
<p>At MUSA, we love to talk about tricky math problems of all levels!
Here's some of our favorite problems. If you can't figure them out yourself,
try asking at office hours and see if anyone else can make heads or tails of them.</p>
<h4>Topological invariants and the open mapping theorem</h4>
<p><strong>Prerequisite</strong>: Math 185; Math 142 or Math 202A will help</p>
<p>Say that a metric space X is locally connected if for each point x of X there is a connected open set U containing x. Let K be a locally connected compact subset of the complex plane <b>C</b> and V(K) denote the vector space of all holomorphic functions V(K) → <b>C</b>. Give a formula for the dimension of V(K) in terms of topological invariants of K.</p>
<p>If that was pretty easy, what happens if K is not locally connected? In particular, what is the dimension of V(K), for K the Cantor set?</p>
<h4>Fractal topology</h4>
<p><strong>Prereqs</strong>: Math 104</p>
<p>If X is a metric space, say that X has a <i>fractal topology</i> if, for each nonempty open set U in X, there is a homeomorphism from U to X. What's an example of X?</p>
<h4>Cuboids on the sphere</h4>
<p><strong>Prereqs</strong>: None</p>
<p>Let S^2 denote the 2-sphere. Describe the space of cuboids (that is, rectangular prisms) whose vertices are all points on S^2.</p>
<h4>Prison break!</h4>
<p><strong>Prereqs</strong>: None</p>
<p>There are N prisoners in a circular prison; each isolated in their own soundproof prison cell. Each prisoner is given a button and a switch; the button controls the lightbulb in the prisoner one cell clockwise from the button-holder. When a prisoner presses their button, the corresponding lightbulb will flash on and then off at the coming noontime, whenever that is. The goal of the prisoners is to find N; the total number of prisoners. To make things challenging; the prison warden shuffles all the prisoners every night.</p><p>Can this be done; given that you are allowed to give an algorithm A for all the other prisoners to follow; and you yourself can follow an algorithm B?</p>
<h4>Towers of boxes</h4>
<p><strong>Prereqs</strong>: None</p>
<p>How many different ways can a person stack n cubical boxes if (a) the person must stack all the boxes in the same two dimensional plane, (b) on the bottom layer of boxes, the boxes must be placed side by side with no gaps in between, and (c) on all higher levels, the boxes must be stacked directly on top of an existing box?</p>
<h4>Homeomorphism classes in <b>R</b><sup>n</sup></h4>
<p><strong>Prereqs</strong>: Math 104</p>
<p>We say that two subsets, X and Y, of <b>R</b><sup>n</sup> are <i>homeomorphic</i> if there is a continuous bijection from X to Y whose inverse is also continuous.</p><p>Show that there exist two subsets of <b>R</b><sup>n</sup> which are not homeomorphic, but do have continuous bijections between them.</p>
</section>
<!-- Footer -->
<div style="clear:both;"></div>
<footer>
<p>
MUSA is a Registered Student Organization acting independently of the
University of California.
We take full responsibility for our organization and this web site.</p>
<p>Report problems with the site to the <a href="officers.html">Curator</a>.</p>
<p>© MUSA 2020</p>
<p>
<a href="https://www.ocf.berkeley.edu">
<img src="img/ocfbadge_mini8dark.png"
alt="Hosted by the OCF" style="border: 0;" />
</a></p>
</footer>
<!-- Google Analytics: change UA-XXXXX-Y to be your site's ID. -->
</div>
</body>
</html>