From 8fac001bd3be16bb67adc6ad1b9c040800c5ac4a Mon Sep 17 00:00:00 2001 From: Trance-0 <60459821+Trance-0@users.noreply.github.com> Date: Mon, 12 Jan 2026 12:55:04 -0600 Subject: [PATCH] updates? --- content/CSE510/CSE510_L14.md | 2 +- content/CSE5313/CSE5313_L8.md | 2 +- content/Math401/Freiwald_summer/Math401_T6.md | 2 +- content/Math4201/Exam_reviews/Math4201_E3.md | 9 +++ content/Math4202/Math4202_L1.md | 17 +++++ content/Math4202/_meta.js | 7 +++ content/Math4202/index.md | 63 +++++++++++++++++++ content/Math4302/Math4302_L1.md | 2 + content/Math4302/_meta.js | 7 +++ content/Math4302/index.md | 63 +++++++++++++++++++ content/_meta.js | 7 +++ 11 files changed, 178 insertions(+), 3 deletions(-) create mode 100644 content/Math4202/Math4202_L1.md create mode 100644 content/Math4202/_meta.js create mode 100644 content/Math4202/index.md create mode 100644 content/Math4302/Math4302_L1.md create mode 100644 content/Math4302/_meta.js create mode 100644 content/Math4302/index.md diff --git a/content/CSE510/CSE510_L14.md b/content/CSE510/CSE510_L14.md index 50e52ce..61b0e76 100644 --- a/content/CSE510/CSE510_L14.md +++ b/content/CSE510/CSE510_L14.md @@ -85,7 +85,7 @@ TRPO = NPG + Linesearch + monotonic improvement theorem Pros - Proper learning step -- [Monotonic improvement guarantee](./CSE510_L13.md#Monotonic-Improvement-Theorem) +- [Monotonic improvement guarantee](../CSE510_L13.md#Monotonic-Improvement-Theorem) Cons diff --git a/content/CSE5313/CSE5313_L8.md b/content/CSE5313/CSE5313_L8.md index 9c04027..5971ebe 100644 --- a/content/CSE5313/CSE5313_L8.md +++ b/content/CSE5313/CSE5313_L8.md @@ -46,7 +46,7 @@ The minimum distance of the extended Hamming code is 4. It is sufficient to show that every 3 columns are linearly independent. -Using the [lemma for minimum distance](./CSE5313_L7#lemma-for-minimum-distance), we have that the minimum distance is 4. +Using the [lemma for minimum distance](../CSE5313_L7#lemma-for-minimum-distance), we have that the minimum distance is 4. Notice that in $\mathbb{F}_2$, multiplication is equivalent to AND operation. diff --git a/content/Math401/Freiwald_summer/Math401_T6.md b/content/Math401/Freiwald_summer/Math401_T6.md index cb0a1cd..18bc350 100644 --- a/content/Math401/Freiwald_summer/Math401_T6.md +++ b/content/Math401/Freiwald_summer/Math401_T6.md @@ -76,7 +76,7 @@ This is a contradiction, so $|\psi^+\rangle$ is entangled. #### Density operator -A density operator is a [Hermitian](./Math401_T5#definition-of-hermitian-operator), positive semi-definite operator with trace 1. +A density operator is a [Hermitian](../Math401_T5#definition-of-hermitian-operator), positive semi-definite operator with trace 1. The density operator of a pure state $|\psi\rangle$ is $\rho=|\psi\rangle\langle\psi|$. diff --git a/content/Math4201/Exam_reviews/Math4201_E3.md b/content/Math4201/Exam_reviews/Math4201_E3.md index 84111ac..44bf039 100644 --- a/content/Math4201/Exam_reviews/Math4201_E3.md +++ b/content/Math4201/Exam_reviews/Math4201_E3.md @@ -635,6 +635,7 @@ A topological space $(X,\mathcal{T})$ is normal if for any disjoint closed sets Some corollaries: 1. $X$ is normal if and only if given a closed set $A\subseteq X$, there is open neighborhood $V$ of $A$ such that $\overline{V}\subseteq U$. +2. Every compact Hausdorff spaces is normal. > [!CAUTION] > @@ -646,4 +647,12 @@ Let $X$ be a regular space with countable basis, then $X$ is normal. *Prove by taking disjoint open neighborhoods by countable cover.* +### Urysohn Lemma + +Let $X$ be a normal space, $A,B$ be two closed disjoint set in $X$, then there exists continuous function: $f:X\to[0,1]$ such that $f(A)=\{0\}$ and $f(B)=\{1\}$. + +#### Urysohn metrization theorem + +If $X$ is normal (regular and second countable) topological space, then $X$ is metrizable. + diff --git a/content/Math4202/Math4202_L1.md b/content/Math4202/Math4202_L1.md new file mode 100644 index 0000000..615591a --- /dev/null +++ b/content/Math4202/Math4202_L1.md @@ -0,0 +1,17 @@ +# Math4202 Topology II (Lecture 1) + +## Topology of manifolds + +### Fundamental groups + +Use fundamental group as invariant for topological spaces up to homeomorphism (exists bijective and continuous map with continuous inverse) / homotopy equivalence. + +Classifying two dimensional surfaces. + +- Sphere +- Torus +- $\mathbb{R}P^2$ + +## Quotient spaces + +Let $X$ be a topological space and $f:X\to Y$ is a continuous, surjective map. WIth the property that $U\subset Y$ is open if and only if $f^{-1}(U)$ is open in $X$, we say $f$ is a quotient map and $Y$ is a quotient space. \ No newline at end of file diff --git a/content/Math4202/_meta.js b/content/Math4202/_meta.js new file mode 100644 index 0000000..f2f3242 --- /dev/null +++ b/content/Math4202/_meta.js @@ -0,0 +1,7 @@ +export default { + index: "Course Description", + "---":{ + type: 'separator' + }, + Math4202_L1: "Topology II (Lecture 1)", +} diff --git a/content/Math4202/index.md b/content/Math4202/index.md new file mode 100644 index 0000000..3506526 --- /dev/null +++ b/content/Math4202/index.md @@ -0,0 +1,63 @@ +# Math4202 + +## Instructor + +Xiang Tang, Cupples I, 112B, xtang@math.wustl.edu +Classroom and Time + +Wrighton Rm 250, MWF, 11:-11:50. + +## Office Hour + +I will hold Zoom Office hour on Tuesday at 4-5 p.m. for both 5222 and 4202. My zoom personal meeting id is 327 569 4749 with access code XiangTang. +I will hold in person office hour on Monday at 1-2 p.m. , Friday 3-4 p.m. (open for both 5222 and 4202). +Write to me to make an appointment if the above time does not work with your schedule or prefer to meet in person. + +## Text + +Topology (2nd Edition), by James Munkres, 537 pages Publication Date: May 2000 Publisher: Prentice Hall. +Prerequisite + +Math 4201 or equivalent + +## Preview + +This is a course about general topology. We will attempt to cover most of Chapters 4, 9, 11, 12, 13. + +## Lectures + +You are strongly recommended to attend the lectures. No talk, food and drinking is allowed in class. Please close your cell phone or change it to ``silent". Information about materials covered and homework assigned every week will be updated on the course website. + +## Exams + +There will be one midterm and one final exam. The following is the schedule + +Midterm Exam March 4th, 11-11:50. Wrighton 250 + +Final Exam (may be presentation) May 6th, 10:30-12:30 Wrighton 250 +Homework + +You will have graded homework turned in every Tuesday by 18:00, (6:00 p.m). Late homework will not be accepted! The homework collected is to be considered a bare minimum of homework that you should do. **"A" students will generally do nearly every problem in the exercise sections.** + +We will use an online system called Gradescope to collect and distribute homework, which you can sign in with your Canvas account. Only PDF and JPEG format files will be accepted by Gradescope. You will need to upload your work for each problem separately. Simply drag and drop your files to the upload areas under the questions or browse to locate them. You can drag between questions, and add or delete pages under each question. Please make sure your pictures are sharp enough to be graded. And please ensure the uploaded pages are in order and rotated correctly if your solution is written on several pages. + +Homework is graded according to the following distribution. Each homework set consists of 5 problems. Each problem counts for 10 points and the total score of a homework is 50 points. +Grading scale + +Homework: 50%, Midterm: 25%, Final: 25%. The grades are assigned according the percentage you are in the class. + +You are expected to take the exams at their scheduled times. If you are away because of a university sporting event or field trip, then you may arrange for your coach or professor to administer the exam. Excused absences may be granted in the case of illness or bereavement. All excused absences must be granted before the exam is taken. The final exam date cannot be changed for reasons of traveling convenience. + +In total, we will collect 10 homework sets. You are allowed to drop the two lowest homework scores. + +You are allowed to discuss with your classmates, friends, and artificial intelligence applications to work on your homework problems. Please make sure that you are writing the final solutions independently. Proper acknowledgements of your discussion with various resources should be stated in your homework solutions. + +Letter grades will be given based on your overall score. The cutoffs for the various letter grades will be no higher than the following: + +| Letter | Score | +|:------:|:-----:| +| A-| 85| +| B-| 75| +| C-|60| +|D|50| + diff --git a/content/Math4302/Math4302_L1.md b/content/Math4302/Math4302_L1.md new file mode 100644 index 0000000..0a6d758 --- /dev/null +++ b/content/Math4302/Math4302_L1.md @@ -0,0 +1,2 @@ +# Math4302 Modern Algebra (Lecture 1) + diff --git a/content/Math4302/_meta.js b/content/Math4302/_meta.js new file mode 100644 index 0000000..0ceaa6f --- /dev/null +++ b/content/Math4302/_meta.js @@ -0,0 +1,7 @@ +export default { + index: "Course Description", + "---":{ + type: 'separator' + }, + Math4302_L1: "Modern Algebra (Lecture 1)", +} diff --git a/content/Math4302/index.md b/content/Math4302/index.md new file mode 100644 index 0000000..3506526 --- /dev/null +++ b/content/Math4302/index.md @@ -0,0 +1,63 @@ +# Math4202 + +## Instructor + +Xiang Tang, Cupples I, 112B, xtang@math.wustl.edu +Classroom and Time + +Wrighton Rm 250, MWF, 11:-11:50. + +## Office Hour + +I will hold Zoom Office hour on Tuesday at 4-5 p.m. for both 5222 and 4202. My zoom personal meeting id is 327 569 4749 with access code XiangTang. +I will hold in person office hour on Monday at 1-2 p.m. , Friday 3-4 p.m. (open for both 5222 and 4202). +Write to me to make an appointment if the above time does not work with your schedule or prefer to meet in person. + +## Text + +Topology (2nd Edition), by James Munkres, 537 pages Publication Date: May 2000 Publisher: Prentice Hall. +Prerequisite + +Math 4201 or equivalent + +## Preview + +This is a course about general topology. We will attempt to cover most of Chapters 4, 9, 11, 12, 13. + +## Lectures + +You are strongly recommended to attend the lectures. No talk, food and drinking is allowed in class. Please close your cell phone or change it to ``silent". Information about materials covered and homework assigned every week will be updated on the course website. + +## Exams + +There will be one midterm and one final exam. The following is the schedule + +Midterm Exam March 4th, 11-11:50. Wrighton 250 + +Final Exam (may be presentation) May 6th, 10:30-12:30 Wrighton 250 +Homework + +You will have graded homework turned in every Tuesday by 18:00, (6:00 p.m). Late homework will not be accepted! The homework collected is to be considered a bare minimum of homework that you should do. **"A" students will generally do nearly every problem in the exercise sections.** + +We will use an online system called Gradescope to collect and distribute homework, which you can sign in with your Canvas account. Only PDF and JPEG format files will be accepted by Gradescope. You will need to upload your work for each problem separately. Simply drag and drop your files to the upload areas under the questions or browse to locate them. You can drag between questions, and add or delete pages under each question. Please make sure your pictures are sharp enough to be graded. And please ensure the uploaded pages are in order and rotated correctly if your solution is written on several pages. + +Homework is graded according to the following distribution. Each homework set consists of 5 problems. Each problem counts for 10 points and the total score of a homework is 50 points. +Grading scale + +Homework: 50%, Midterm: 25%, Final: 25%. The grades are assigned according the percentage you are in the class. + +You are expected to take the exams at their scheduled times. If you are away because of a university sporting event or field trip, then you may arrange for your coach or professor to administer the exam. Excused absences may be granted in the case of illness or bereavement. All excused absences must be granted before the exam is taken. The final exam date cannot be changed for reasons of traveling convenience. + +In total, we will collect 10 homework sets. You are allowed to drop the two lowest homework scores. + +You are allowed to discuss with your classmates, friends, and artificial intelligence applications to work on your homework problems. Please make sure that you are writing the final solutions independently. Proper acknowledgements of your discussion with various resources should be stated in your homework solutions. + +Letter grades will be given based on your overall score. The cutoffs for the various letter grades will be no higher than the following: + +| Letter | Score | +|:------:|:-----:| +| A-| 85| +| B-| 75| +| C-|60| +|D|50| + diff --git a/content/_meta.js b/content/_meta.js index de276b2..230e432 100644 --- a/content/_meta.js +++ b/content/_meta.js @@ -52,6 +52,13 @@ export default { timestamp: true, } }, + Math4202: { + title: 'Math4202', + type: 'page', + theme:{ + timestamp: true, + } + }, Math416: { title: 'Math416', type: 'page',