# Math 54 Online Guidelines ## Final exam (timed 1130AM) clarifications and corrections 1. Whenever it says 'find a matrix with nonnegative entries (i.e., $\ge 0$)' this means that **all** the entries should be nonnegative 2. Both questions are worth 5pts on the AM6 exam (there was a typo saying the second question was 1pt). ## Final Exam (36-hr part) clarifications and corrections 0. If you did not submit the cheat sheet on time, you can still submit it late and receive a partial credit of $3/5$. 1. Question 6c used to say "find a vector $x$..." but it now says "find a **nonzero** vector $x$...". 2. In Question 2.10-11, a "function from $\mathbb{R}$ to $\mathbb{R}$" is the same thing as a function $f:\mathbb{R}\rightarrow\mathbb{R}$. 3. In Question 5c, the matrix A is the same one from part 5b. 4. In Question 9c, the function f is the same one as in 9ab. 5. In Question 6, 'truncated SVD' just means find a factorization $A=U\Sigma V^T$ in which $\Sigma$ is square and $U$ and $V$ hare orthonormal columns. ## Final Exam The exam will consist of three parts: 0. Cheat Sheet (5%), due at 11:30am PDT on 5/14 on Gradescope. May be written on paper or using a tablet. 1. Untimed part (80% questions + 5% honor code), posted at 11:30am PDT on 5/14, due at 11:30pm PDT on 5/15 (i.e., 36 hours). Must be handwritten on actual paper and submitted via scan/picture on Gradescope. 2. Timed part (10%, consisting of two questions of the type on Q2 of the midterms, 35min): choose 11:30am PDT or 11:30pm PDT on 5/15. Must be handwritten on actual paper and submitted via scan/picture on Gradescope. **DSP**: DSP students will be given extra time for the timed part (2) only, and may submit their assignments "late" on Gradescope after 1.5x or 2x the alotted time. THe untimed portion will be due at the same time for all students, regardless of DSP accommodations. ## General Instruction has been moved online for the rest of the semester. This document will contain the most up to date information regarding how it will be handled. **Lecture** Will be held on Zoom 5-630pm PST on TTh. See the bCourses "syllabus" page for a link to the Zoom meeting, as well as links to recordings of all online lectures in case you miss them. **Section** Will be held on Zoom, at the same times as before, which are listed [here](https://math.berkeley.edu/courses/spring-2020-math-54-002-lec). All of the GSI Zoom IDs are on bCourses under "syllabus". **Office Hours**, both mine and the GSIs', will be held on Zoom at the same times as before, as listed on the course webpage. **Quizzes** Will be held on Wednesdays. Quizzes will be released at 8am PST on Wednesdays and Gradescope will be open *for 24 hours* until 8am PST on Thursdays for submission. Quizzes are open book and open notes. **Homework** Will be assigned and collected online as before, due midnight PST on Tuesdays. **Exams** MT2 and the final will be held as scheduled, online. **MT2 Details** New Midterm 2 Guidelines: 1. Midterm 2 will be released at 8am PST on 4/7 and open for 24 hours, on Gradescope. Answers must be submitted by 8am PST on 4/8. The exam will be open book and not timed. This window will accommodate people from all time zones, and there will be no extensions for DSP students since there is effectively no time limit (the test will be just the length of a usual midterm, i.e., 7 questions). 2. The format of the test will be similar to the three practice midterms, except the questions will be on Gradescope rather than on paper. You will have to upload a separate file (image or PDF) for each written question. The flip side is that without time pressure, we will expect answers to be very clearly and thoughtfully written. In order to encourage you to study and collect your thoughts in advance, and because it will be helpful in preparing for the test, we will collect a mandatory 1 page "cheat sheet" from each student on Gradescope before the test begins (i.e., before 8am on 4/7). This sheet will only be graded for completeness (on a 0/1 scale), will be worth 5% of the exam, and must be neatly written. 3. The test will not be curved, so you do not have to worry about other people cheating. Announcement on BC regarding MT2: 1. One of the questions requires you to handwrite the following text on a blank sheet of paper, sign and date it, and upload a scan/photo of it. "As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others. All of the work submitted here is mine, and I have not discussed the content of this exam with any other person. I have not consulted any resources beyond the course materials and my notes during the exam. I have not used calculators, computers, or the internet to do calculations or look up answers." 2. In addition to true/false questions and the honor code above, there are five non multiple-choice questions on the exam, one of which has four parts. For these questions, you must * neatly handwrite* each answer on a separate piece of paper (e-paper and tablets are not allowed) and upload a *separate* scan/photo for each question. This means you will need a total of *nine* sheets of paper (one for the honor code, eight for the remaining questions). Note that both PDF and all picture/photo formats (JPG, PNG, etc.) are accepted, so use whichever is most convenient. After uploading, be sure to check that your file uploaded correctly. (Those with intermittent internet may want to print the exam at the beginning of the day, work on it offline, and upload later when they are done.) 3. Do not ask any questions about the exam on Piazza (note also that anonymous commenting has been disabled). If you have any questions, email or send a private message to me or your GSI. 4. Please submit all answers in PDF or JPG. If you submitted an answer in another format (such HEIC, PNG) already that is fine, but please use these for the remainder. Also, please use actual paper to write your answers, not an iPad or tablet. Answers should be properly oriented since there is no way to rotate them within gradescope while grading. Grid or lined paper is also fine. It is alright to submit more than one page for a single answer if you need it. **Changes to Course policy:** 1. The bottom **three** HW and Quizzes will be dropped. 2. HW7 will be due on Friday 3/20 at midnight, rather than Tuesday.
Last changed by  
 
knikct
4898

Read more

JMM 2023 Special Session: Perspectives on Eigenvalue Computation

The official schedule is posted at https://www.jointmathematicsmeetings.org/meetings/national/jmm2023/2270_program_ss94.html#title The Zoom link for virtual attendance/virtual talks is: https://berkeley.zoom.us/j/94982941411?pwd=RWRXeVdoZUNVTmdqK1FIMksrZFllZz09 Friday, January 6 (101 Hynes Convention Center) 1-2pm: Matt Colbrook, The foundations of infinite-dimensional spectral computations (Zoom) 2-3pm: Josué Tonelli-Cueto, Condition-based Low-Degree Approximation of Real Polynomial Systems

1/3/2023
Math 55 Definition List

Lecture 1: Propositional Logic A proposition is a declarative sentence that is either true or false but not both. A proposition has a truth value which is either $T$ or $F$. A letter used to denote a proposition is called a propositional variable. If $p$ is a proposition, the negation of $p$, denoted $\lnot p$, is the proposition "it is not the case that $p$". The truth value of $\lnot p$ is the opposite of that of $p$. If $p$ and $q$ are propositions, the conjunction of $p$ and $q$ (denoted $p\land q$) is the proposition "p and q." Its truth value is $T$ when both $p$ and $q$ are $T$, and it is $F$ otherwise. If $p$ and $q$ are propositions,he disjunction of $p$ and $q$ is the proposition "p or q". Its truth value is $T$ when at least one of $p$ or $q$ is $T$, and $F$ if both $p$ and $q$ are $F$. If $p$ and $q$ are propositions, the conditional $p\rightarrow q$ is the proposition "if $p$ then $q$". Its truth values are given by the following truth table (which lists its truth values in terms of those of $p$ and $q$): [see Table 5 in Rosen] The converse of $p\rightarrow q$ is $q\rightarrow p$. A compound proposition consists of logical operations (the four listed above) applied to propositions or propositional variables, possibly with parentheses. The truth value of a compound proposition can be mechanically determined given the truth values of its constituents.

12/12/2022
Math 55 Fall 2022 Graph Theory Notes

Lecture 14 Basic Terminology, Handshaking Theorem A graph is a pair $G=(V,E)$ where $V$ is a finite set of vertices and $E$ is a finite multiset of $2-$element subsets of $V$, called edges. If $E$ has repeated elements $G$ is called a multigraph, otherwise it is called a simple graph. We will not consider directed graphs or graphs with loops (edges from a vertex to itself). Two vertices $x,y\in V$ are adjacent if ${x,y}\in E$. An edge $e={x,y}$ is said to be incident with $x$ and $y$. The degree of a vertex $x$ is the number of edges incident with it. Theorem. In any graph $G=(V,E)$, $$ \sum_{v\in V} deg(v) = 2|E|.$$ Proof. Let $I={(e,v):e\in E,v\in V,\textrm{$e$ is incident with $v$ in $G$}}$ be the set of edge-vertex incidences in $G$. We will count the number of incidences in two ways: (i) Observe that every edge participates in exactly two incidences, and no incidence participates in more than one edge. Thus, the total number of incidences is $|I|=2|E|$.

12/12/2022
Math 55 Graph Theory Practice Questions

Prove that every simple graph with $n$ vertices and $k$ edges has at least $n − k$ connected components (hint: induction, or contradiction). Let $p\ge 3$ be a prime. Consider the graph $G=(V,E)$ with $V={0,1,2,\ldots, (p-1)}$ and $$E={{x,y}:x-y\equiv 2(mod p)\lor x-y\equiv -2 (mod p)}$$ Show that $G$ is connected. Does $G$ have an Euler circuit? Prove your answer. Let $n\ge 1$ be an integer and let $k\le n/2$. Consider the graph $G=(V,E)$ with $V={S\subseteq {1,2,\ldots,n}: |S|=k}$ and $$E = {{S,T}:|(S-T)\cup (T-S)|=1}.$$ What are the degrees of the vertices in $G$? Is $G$ connected? For which values of $n$ and $k$ does $G$ have an Eulerian circuit? For which values of $n$ and $k$ is $G$ $2-$colorable? Prove your answers.

11/8/2022
Read more from knikct
Published on HackMD