ossu/math

🧮 Path to a free self-taught education in Mathematics!

math's Issues

FYI: UCCS Video Course Archive

UCCS Video Course archive has nearly complete coverage of in-major math courses, and a little poking around on professor web pages will usually get you course materials to go with them.

UCCS is apparently world-renowned for their freely-available online video math courses shot in PanOpto 2-perspective view, so you can see the boardwork and the notes at the same time.

https://math.uccs.edu/course-resources-detail/vidarchive

RFC : Addition of Combinatorial Mathematics

Problem:
Addition of Prbobaility and Statistics courses in its Advanced Maths

Duration:
April 07, 2022.

Background:
OSSU promises the equivalent of education an undergraduate education in Mathematics. To evaluate our recommended courses, we use the CUPM 2015 guideline that specifies the number of mathematical areas a student should cover.

We will be referring to Discrete Math and Combinatorics document here.

Two courses that CUPM 2015 recommend to cover combinatorial studies

1. Enumerative Combinatorics
2. Graph Theory

Originally this RFC was meant to propose two courses that were on Coursera but were taken down recently. So I will be referring textbook to cover above material

To cover both these courses a open textbook by Mitchel T. Keller, William T. Trotter is recommended by me

Applied Combinatorics

The book was also used to teach students applied combinatorics to students at Georgia Tech. Few reviews about the textbook can be found here.

Now rest of the courses were inspired by CUPM 2015 Applied Math track and MIT Applied Math Track and are of great quality that cant be ignored

The document can be referred here Applied Mathematics

What CUPM 2015 suggests :

Discrete applied mathematics. This area draws on or includes mathematical programming (in linear, integer, and binary forms), graph and network theory, scheduling, error correction systems, data compression systems, etc. Because discrete applied mathematics has emerged relatively recently, courses related to that field may have a greater variety of titles than we find in classical applied mathematics. These include Cryptography, Operations Research (which may also includes tools from continuous mathematics), Discrete Optimization, Linear Programming, Network Science, Graph Theory, Combinatorics, Game Theory, Social Choice, etc.

MIT offeres following in their applied math curriculum as electives

1. Algebraic Combinatorics
2. Analysis of Algorithms
3. Analytic Combinatorics
4. Combinatorial Optimization

ALGEBRAIC COMBINATORICS

This course is offered by premier institutes of India i.e, Institute of Mathematical Sciences with Indian Institute of Technology Madras. The course is short and is of 7 weeks meant to prepare students for post-grad school and is more math-oriented course rather than applied math course.

Algebraic Combinatorics

ANALYSIS OF ALGORITHMS AND ANALYTIC COMBINATORICS

Two following courses that go hand in hand are by Prof Robert Sedgewick.

Analysis of Algorithms , Review of the course

Analytic Combinatorics , Review of the course

The Analysis of Algorithms may seem like a CS class but is actually a math class. Both the courses are offered as Analytic Combinatorics in Princeton with Analysis of Algorithms as part 1 of the course.

Also Game Theory 1 is pre-requisite mentioned in RFC #24.

One review of Analysis of Algorithms mentioned "This course is more about mathematic than algorithms, it teaches how to solve tricky combinatorial problems"

DISCRETE OPTIMIZATION

This course is of very high quality and is great reviewed

Discrete Optimization , Review of the course

The course is for skilful programmers who know algorithms but teaches optimization technology very well.

The four above courses are bit extra than what CUPM 2015 recommend but are of very high quality and useful to both OSSU-CS students who would like to do some math classes or OSSU- Math students who would like to have applied math class oriented towards CS.

Proposal

Add courses as following

Discrete and Combinatorial Math

Applied Combinatorics is equivalent to two courses i.e, Enumerative Combinatorics and Graph Theory

Courses	Duration	Effort	Prerequisites
Applied Combinatorics	16 weeks	10-12 hours/week	Introduction to Mathematical Thinking, Mathematics for Computer Science , Linear Algebra and Intro to Analysis . Also checkout Background Material for Combinatorics
Algebraic Combinatorics	8 weeks	4-5 hours/week	Mathematics for Computer Science, Intro to Abstract Algebra and Linear Algebra
Analysis of Algorithms , Textbook	9 weeks	7-8 hours/week	Intro to Comp Sci, Mathematics for Computer Science, Game Theory 1, Intro to Algorithms (or any other Algorithm class)
Analytic Combinatorics, Textbook	8 weeks	7-8 hours/week	Analysis of Algorithms
Discrete Optimization	8 weeks	12-14 hours/week	Intro to Comp Sci, Mathematics for Computer Science, Intro to Algorithms (or any other Algorithm class) and Linear Algebra

Why MIT Intro to Algorithms as pre-requisite. MIT uses Python for Intro to Algorithms which is also an important language for Data Science and Statistical Area where Applied Math students will be benefited.

End Note
Where topics like Abstract Algebra, Logic and Geometry gives a perspective of pure math
Probability, Statistics + Combinatorial Math gives a perspective for applied math

Lets add a LaTeX course

Sort of like how we have "The missing semester of Your CS Education" under CS, we should consider having a LaTeX course in this track. I'm not sure of any good latex courses though

Request for Comment : Add Introduction to Abstract Algebra (Group Theory) under Core Mathematics

Problem:
OSSU Math does not introduce abstract algebra in its core curriculum

Duration:
January 07, 2022.

Background:
OSSU promises the equivalent of education an undergraduate education in Mathematics. In order to evaluate our recommended courses, we use the CUPM 2015 guideline that specifies number of mathematical areas a student should cover.

Let us visit Abstract Algebra section of CUPM 2015.

What CUPM 2015 says about Algebra A (Intro to Abstract Algebra)

This course offers what we feel is a standard model for a first-semester Abstract Algebra course suitable for nearly every college or university. We feel some tension between the breadth of a first course that includes both groups and rings and the depth of one that focuses only on groups or only on rings. One argument for breadth is that both rings and groups are implicit in the pre-collegiate curriculum, and we feel that every student would benefit from an opportunity to see these concepts developed. For example, pre-college students encounter the rings of integers, rational numbers, real numbers, polynomials etc. and they will probably have also seen various groups of symmetries, both in the elementary grades and in high school geometry. We thus recommend that this one-semester course should cover both groups and rings, and also (lightly) fields. A disadvantage of this breadth is, of course, that the student has less opportunity to explore a single structure in depth. For this reason, some institutions might wish to offer an alternative first Abstract Algebra course that focuses more deeply one area: for example finite group theory. Such a course might start with definitions and examples, and eventually reach a proof of the Sylow existence theorem, and perhaps more.

The order of the topics can be chosen to suit the instructor’s preference. Whichever of groups or rings is studied first, the student has the experience of learning one structure and then seeing the parallels in the second. (The analogy we make is to learning a computer language, and then the empowerment that comes with the realization of how much easier it is to learn a second language.) Our study group prefer groups first, because of their simpler definition (only one binary operation and fewer axioms) and because the familiarity of the integers and the real numbers can hide from students which statements require proof. On the other hand, we recognize that some instructors prefer to begin with rings exactly because of their familiarity to students. Studying rings first also provides some useful facts about the integers such as the division algorithm and properties of the greatest common divisor.

Topics covered under the suggestion

Groups

• Definitions and examples of groups and subgroups.
• Cyclic groups and their subgroups, and the orders of elements.
• Symmetric groups, cycle notation, parity of a permutation and the alternating group.
• Isomorphisms and Cayley’s Theorem. (See the remarks below.
• Cosets and Lagrange’s Theorem, the falsity of the converse of Lagrange’s Theorem, and if time permits, the statement of the Sylow existence theorem.
• Group actions. (See the remarks below.)
• External direct products, if time permits.
• Normal subgroups and factor groups, conjugates of a subgroup and of an element.
• Homomorphisms, and the Fundamental Homomorphism Theorem

Rings

• Definitions and examples of rings and fields.
• Ideals and factor rings.
• Principal ideals, integral domains, principal ideal domains, maximal and prime ideals.
• Homomorphisms, the Fundamental Homomorphism Theorem, the theorem that a com- mutative ring modulo a maximal ideal is a field.
• Polynomial rings and irreducible polynomials.

Topics covered by course

• Motivation, definition, examples and basic properties
• Subgroups, subgroups of integers, homomorphisms
• Quotient groups, isomorphism theorems
• Group operations, counting formula
• Symmetric groups
• Operations of a group on itself, class equation
• Sylow theorems I
• Sylow theorems II

The course does not cover rings as an introduction but goes well around in depth covering groups.

As mentioned CUPM 2015 Abstract Algebra guideline

A disadvantage of this breadth is, of course, that the student has less opportunity to explore a single structure in depth. For this reason, some institutions might wish to offer an alternative first Abstract Algebra course that focuses more deeply one area: for example finite group theory.

Proposal:
Add these course to core Math curriculum as Introduction to Abstract Algebra(Group Theory)

• Introduction to Abstract Algebra(Group Theory)

The course also has its syllabus page that specifies pre-requisites of the course, introduction to instructor and topic that will be covered.

Pre-Requisite for the course that is mentioned is high school mathematics although I recommend Linear Algebra to be its co-requisite.

The course has also its own book and set of assignments that can be accessed via course site.

This course will take duration of 8 weeks with effort of 6-7hours/week to complete.

Calculus 1A: Differentiation is no longer available at eDx

Calculus 1A: Differentiation is no longer available at eDx.
Please, provide equivalent alternative for this course.

As far as I understand, copy of this course is available for free here: https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.1x+2T2019/course/ although, there's no way to get a certificate.

Petition to add commutative algebra

Commutative algebra is the study of commutative ring and is a ticket to a lot of modern mathematics. For example, homological algebra, algebraic number theory, algebraic geometry, arithmetic geometry, Diophantine geometry. It is impossible for a algebra-focused student to continue without the study of commutative algebra. This is the reason I open this issue.

Which year and prerequisite?

In the book Introduction to Commutative Algebra by Michael Atiyah and I. G. MacDonald, the introduction said

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of providing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra.

Resources

One of the most classics out there is Introduction to Commutative Algebra by Michael Atiyah and I. G. MacDonald. I have found PDF file here. It was uploaded publicly by a professor from Université Claude Bernard Lyon 1, so it's not likely to be some violation of copyright (If it is piracy let's find equivalences somewhere else). There is a discussion on the prerequisite of this book on stackexchange

There is a list that strictly follow the book mentioned above (final two chapters are missing though): https://www.youtube.com/watch?v=VKxT2lkmMVE&list=PLq-Gm0yRYwTjBziGqSW9kFF9o2l5ECDvY

Another list but it follows a different book (Commutative Algebra - with a View Toward Algebraic Geometry): https://www.youtube.com/watch?v=QOTf8KfrZFU&list=PL8yHsr3EFj53rSexSz7vsYt-3rpHPR3HB

Of course I'm always open to discuss further. Hope it helps!

Request to add optional courses for Calculus

Hi,

The courses offered through edx are instructor timed. That makes it difficult to start. Calculus 1A was already started and ends on sept 2. I will need to wait for it's offering again. Since it's a series, i can't take other courses in series before taking the prerequisite course 1A ( even though i can, i should not without the prerequisites to completely understand the course )

Is there a possibility to give equivalent course here which are self-paced ?

RFC : Addition of Probability and Statistics courses in Advanced Math

Problem:
Addition of Prbobaility and Statistics courses in its Advanced Maths

Duration:
March 19, 2022.

Background:
OSSU promises the equivalent of education an undergraduate education in Mathematics. To evaluate our recommended courses, we use the CUPM 2015 guideline that specifies the number of mathematical areas a student should cover.

We will be referring to two docs here Probability and Stochastic Process and Applied Statistics and Data Analysis

Introducing Second Probability Course : Stochastic Process

What CUPM 2015 says

A second undergraduate probability course, if offered at all, is usually about stochastic processes. Stochastic processes are important in operations research, applied mathematics, computer science, actuarial science, engineering, and financial mathematics. Either version of the probability course can be a prerequisite, although obviously the stochastic process-oriented version is better.

In this course, students should formulate models, gain analytical skills, perform and analyze simulations, and present results to others. They should be encouraged to use computational tools where appropriate and to follow more involved proofs than in the prior (required) probability course. For more about a stochastic operations research course, see the Operations Research Program Area report.

To learn Stochastic Processes I recommend this course
Stochastic Processes

Few reviews of this course is here
Reviews

Now lets come to a statistics course. OSSU does not lack a statistics course but does lack a data analysis course.

What CUPM 2015 says

For students majoring in the mathematical sciences, we recommend a course focused on applied data analysis and driven by real data. The course should stress conceptual understanding, foster active learning, and introduce students to statistical technology. The focus should be on the effective collection and analysis of data, along with appropriate interpretation and communication of results.

Just as Mathematics Departments routinely do with calculus courses, such a course in Applied Statistics can serve a wide audience. Also as with calculus, some institutions will have one level of the course while other larger institutions might have different courses for different audiences. In every case, however, the focus should be on understanding effective data analysis rather than on the underlying mathematical theory

One course they recommend is Applied Statistics focusing on Data Analysis

Course Outline:
● Data collection, including random sampling and design of experiments (2 weeks)
● Data description, including graphs and summary statistics for categorical and quantitative
variables and relationships between variables (2 weeks)
● Introduction to the key ideas of estimation and testing, using modern resampling methods to
build conceptual understanding (3 weeks)
● More on confidence intervals and hypothesis tests, using the normal and t distributions (3
weeks)
● Advanced tests, as time permits, such as chi-square tests, ANOVA, regression tests, multiple
regression (3 weeks)

I recommend this course to study Data Analysis
Data Analysis

The course covers
Week 1: Introduction to data science and Calculations with R Software
Week 2: Basic Fundamentals of Sampling
Week 3: Simple Random Sampling
Week 4: Simple Random Sampling with R
Week 5: Stratified Random Sampling
Week 6: Stratified Random Sampling with R
Week 7: Bootstrap Methodology with R
Week 8: Introduction to Linear Models and Regression and Simple linear regression Analysis
Week 9: Simple Linear Regression Analysis with R
Week 10: Multiple Linear Regression Analysis
Week 11: Multiple Linear Regression Analysis with R
Week 12: Variable Selection using LASSO Regression

Only drawback of the course you need to know R Programming for which I will recommend this course by same instructor
R Programming

Following two courses will cover the knowledge of Game Theory which will also be an pre-requisite for Combinatorial Math course that i am going to recommend in future

Game Theory
Game Theory II

Proposal

Add the above courses as following

Probability and Statistics

Courses	Duration	Effort	Prerequisites
Discrete Stochastic Process	12 weeks	5-6 hours/week	Probability
Statistical Learning	12 weeks	4-5 hours/week	Beginning Computer Science with R, Probability and Applied Statistics
Game Theory	8 weeks	4-5 hours/week	Probability and Calculus 1C
Game Theory II	5 weeks	5-6 hours/week	Game Theory

Alternatives

Stochastic processes

Data Analysis and R Programming

books as an alternative for the lack of adequate courses in Advanced Topics

would it be possible for people with deep knowledge of mathematics to at least suggest a few books as an alternative to courses in Advanced Topics that are lacking adequate courses?

it would be of great help, I assume people will just google for courses or books and get guidance elsewhere but I thought it would be helpful given the trust we have for ossu for the book recommendations to come from this repo

Petition to add Courses/texts in Advanced Topics

Advanced Topics

Mathematical Logic

1. Logic
   Pre-requisite : Intro to Analysis, Intro To Abstract Algebra (Group Theory)
   I recommend these lectures from UC Berkeley

2. Set Theory
   Pre-requisite: Intro to Analysis, Intro To Abstract Algebra (Group Theory)
   I recommend these lectures from UC Berkeley

3. Proofs
   I recommend these lectures

4. Number Theory
   Pre-requisite : Introduction to Abstract Algebra
   I recommend these lectures from Indian Institute of Technology Bombay

Geometry

1. Euclidean Geometry
   Pre-requisite: Calculus 1C by MIT
   For Euclidean Geometry I would recommend this Textbook by Anton Petrunin from Pennsylvania State University.

2. Non-Euclidian Geometry
   Non-Euclidian Geometry can be divided in three parts

• Projective Geometry
  Recommend Pre-requisite : Linear Algebra
  For Projective Geometry I recommend this textbook and I recommend these lectures as additional supplementary lectures.

• Hyperbolic Geometry and Elliptic geometry
  Pre-requisite :Linear Algebra and Multivariate Calculus
  I recommend these lectures by UNSW Sydney

3. Point-Set Topology
   Also Knows as Introductory Topology/General Topology
   Pre-Requisite : Intro to Analysis and Metric Spaces
   Before Point Set Topology I recommend studying Metric Spaces by Oxford Mathematics and then watch these lectures on general topology

Probability and Statistics

1. Combinatorics
   Pre-requisite: Basic Logic and Set Theory
   I recommend these lectures for Combinatorics

2. Game Theory
   I recommend this MOOC from Stanford and UBC

Abstract Algebra

1. Abstract Algebra
   Pre-requisite : Group Theory
   This lecture series was held at liberty University and is in two parts. Abstract Algebra 1 and Abstract Algbera 2

2. Commutative Algebra
   A petition raised by @Admiraldesvl to add Commutative Algebra into Math Curriculum
   Pre-requisite : Linear Algebra, Abstract Algebra 1 and 2
   I recommend this lecture series and this textbook with it.

3. Algebraic Geometry
   Pre-requisite : Commutative Algebra
   I recommend this Algebraic Geometry 1 series by Richard E Borcherds from UC Berkeley and also Algebraic Geometry 2

4. Category Theory
   I will recommend this MOOC by MIT

5. Topology/Algebraic Topology
   Pre-Requisite : Point-Set Topology/ General Topology
   I recommend this lecture series by Prof NJ Wildberger at UNSW Sydney

Mathematical Analysis

1. Real Analysis
   Pre-requisite : Introduction to Analysis
   I will recommend the Real Analysis series by IIT Madras Real Analysis Part 1 And Real Analysis part 2

2. Numerical Analysis
   pre-requisite : Calculus 1C, Linear Algebra, Introduction to Differential Equations and Multivariate Calculus
   Numerical Analysis lecture series by IIT Madras.

3. Complex Analysis
   Pre-requisite : Real Analysis and Linear Algebra
   I found this lecture by IIT Madras to be good
   An another alternative series can be Complex Analysis Fall 2018

Please add these lectures and texts in math curriculum

Calculus links broken

Hi,

I found the calculus links on edx to be broken/not accessible. It would be great if the document can be updated with a new link.

Thanks

Request for Comment : Addition of Geometry Courses in Core and Advanced OSSU/Math

Problem:
OSSU Math does not introduce geometry in its core curriculum and does not recommend any texts/courses in its Advanced Math

Duration:
January 12, 2022.

Background:
OSSU promises the equivalent of education an undergraduate education in Mathematics. In order to evaluate our recommended courses, we use the CUPM 2015 guideline that specifies number of mathematical areas a student should cover.

Let us visit Geometry section of CUPM 2015.

CUPM 2015 basic recommendations state that

Every mathematics department should offer at least one undergraduate course devoted primarily to geometry. There will probably never be a consensus on what that course should cover. However, in Section 6 we offer sample syllabi for some of the many valid course choices that institutions might make. We also outline in Section 4 some of the important issues institutions should consider as they decide which geometry course, or courses, to offer.

Reference : CUPM 2015 Page 1

Let us jump to Section 6 for sample syllabi

One such course is A Survey of Geometries This course aims for breadth, while sacrificing some depth. It assumes that students do remem- ber some of the Euclidean geometry they learned in high school. The level of rigor is purposefully sacrificed in order to develop intuition and to cover some of the breadth of geometry.

Topics covered under this suggestion

• Euclidean geometry
• Analytic geometry
• Hyperbolic geometry
• Spherical geometry
• Transformations
• Symmetries
• Projective geometry

Reference : CUPM 2015 Geometry Page 11

I suggest this book Euclidean Plain and Its Relatives for such a course

This book is meant to be rigorous, conservative, elementary, and mini- malist. At the same time, it includes about the maximum what students can absorb in one semester.Approximately one-third of the material used to be covered in high school, but not anymore.
The present book is based on the courses given by the author at the Pennsylvania State University as an introduction to the foundations of geometry. The lectures were oriented to sophomore and senior university students. These students already had a calculus course. In particular, they are familiar with real numbers and continuity. It makes it possible to cover the material faster and in a more rigorous way than it could be done in high school.

If we look at the Table of Contents of the book it covers

• Euclidean Geometry
• Hyperbolic Geometry
• Spherical Geometry
• Projective Geometry etc.

This book perfectly suits what above CUPM course suggests and can act as a foundation for advanced geometry courses.

Geometry Advanced Courses/Books

Upon reviewing the CUPM 2015. The resources to cover advanced courses in Advanced Geometry

To Learn Euclidean Geometry the book by Sir Euclid 's Euclid Elements is best in itself. A argument that can be raised here
Is It still worth it to study Euclid Elements today? To support this argument I suggest to read this quora answer

For Non-Euclidean Geometry I suggest this book Geometry with an Introduction to Cosmic Topology

What CUPM suggests
Non-Euclidean geometries. The discovery of non-Euclidean geometries was a foundation-shaking event in the history of mathematics. All mathematics majors, with the possible exception of those specializing in certain applied subdisciplines, should know about these developments and how they changed the human understanding of the relationship between mathematics and the real world. This could be part of a geometry course or it could be studied in some other course (such as a history of mathematics course). Ideally, students should know the examples of hyperbolic, elliptic, and spherical geometries.

About the book
From the preface:
Geometry with an Introduction to Cosmic Topology offers an introduction to non-Euclidean geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big? This text is intended for undergraduate mathematics and physics majors who have completed a multivariable calculus course and are ready for a course that practices the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also particularly suited to independent study, with essays and other discussions complementing the mathematical content in several sections.
Contents
An Invitation to Geometry
The Complex Plane
Transformations
Geometry
Hyperbolic Geometry
Elliptic Geometry
Geometry on Surfaces
Cosmic Topology

Also the review by MAA calls it “a masterfully written textbook.”

Another course suggested by CUPM 2015 is Differential Geometry

6.7 Differential geometry
The undergraduate differential geometry course should include theoretical and computational com- ponents, intrinsic and extrinsic viewpoints, and numerous applications:
18
• Geometry of curves in space, including the Frenet frame
• Theory of surfaces, including parameterizations, first and second fundamental forms, curva-
ture and geodesics
• The concluding part of the course could be a focus that depends on the interest of the instructor and students, such as the Gauss-Bonnet Theorem, the theory of minimal surfaces, or the geometry of space-time with applications to general relativity.
Ideally a course in differential geometry allows students to see the connections between such topics as calculus, geometry, spatial visualization, linear algebra, differential equations, and complex variables, as well as various topics from the sciences, including physics. The course may serve as an introduction to these topics or a review of them. The course is not only for mathematics majors—it encompasses techniques and ideas relevant to many students in the sciences, such as physics and computer science.

For this topic I suggest this book
A Course in Differential Geometry by SHARIPOV R.A.

What book says

This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject. This book is devoted to the first acquaintance with the differential geometry. Therefore it begins with the theory of curves in three-dimensional Euclidean space E. Then the vectorial analysis in E is stated both in Cartesian and curvilinear coordinates, afterward the theory of surfaces in the space E is considered. The newly fashionable approach starting with the concept of a differentiable manifold, to my opinion, is not suitable for the introduction to the subject. In this way too many efforts are spent for to assimilate this rather abstract notion and the rather special methods associated with it, while the the essential content of the subject is postponed for a later time. I think it is more important to make faster acquaintance with other elements of modern geometry such as the vectorial and tensorial analysis, covariant differentiation, and the theory of Riemannian curvature. The restriction of the dimension to the cases n = 2 and n = 3 is not an essential obstacle for this purpose. The further passage from surfaces to higher-dimensional manifolds becomes more natural and simple.

Topics Covered by the book follows a lot what CUPM 2015 suggests.

Proposal

Add the above texts as following

Core Mathematics

Geometry

Courses	Duration	Effort	Prerequisites
Euclid Plain and Its Relatives	20 weeks	3-5 hours/week	Elementary Set Theory and Calculus 1C

Advanced Mathematics

Geometry

Courses	Duration	Effort	Prerequisites
Euclid Elements	13 weeks	6-8 hours/week	Mathematical Maturity
Geometry with an Introduction to Cosmic Topology	16 weeks	7-8 hours/week	Multivariable Calculus
Differential Geometry	8 weeks	4-5 hours/week	Multivariable Calculus

Logic Course to Evaluate

I think we should investigate using https://www.coursera.org/learn/logic-introduction as the required logic course. It's a little more focus on generic logic vs math logic, but I think it still applies. I'd love to hear some thoughts.

No clear-cut best option for Introductory Real Analysis course

BLUF: I've been racking my brain trying to find a 1) good 2) free 3) introductory course in Real Analysis 4) with video lectures, 5) assignments and 6) an easily accessible book 7) that isn't Rudin. I want this to go in the OSSU Core Mathematics slot for Intro To Analysis.

I need some help.

Details: To clarify:

1. good = acceptably high quality for inclusion in OSSU.
2. free = acceptably low price for inclusion in OSSU; freemium courses considered.
3. introductory course = suitable for a beginner to self-study. No senior-level/grad work, no starting assumption of topology.
4. with video lectures = Watching somebody write proofs on the board -- preferably that match the topic, assignments and book!
5. assignments = a selection of homework practice, preferably with worked proofs and solutions.
6. an easily accessible book = one that's open-source, or that's still in print and readily available for free or a reasonable price.
7. that isn't Rudin = it's a high-quality text for the junior/senior major level, but painfully unapproachable if you're still learning how to work proofs. MIT finds it too difficult for a first book for MIT math majors with instructor and TA support. How are we going to recommend first-timers self-study it??

Here's what I've found so far, loosely ordered from Most to Least Complete:

Introduction to Real Analysis at Bethel University -- has 1, 2, 3, 4, 5, 7.

This is taught by Professor Bill Kinney (https://infinityisreallybig.com) at Bethel University specifically as a first course for majors. It is a gentle introduction to the proof and he states that this course alone may not be enough preparation for grad school, indicating it's not a Real Analysis 1 course for upperclassmen. Additional course materials were recently made available by the instructor at https://drive.google.com/drive/folders/1QtcZHip4x8_hxc1gACgWsHDfdngo36Vj?usp=sharing. By all respects it looks like a great option, but the book is Gordon 2e which runs $120 and there aren't many used ones in circulation.

MIT 18.100A -- has 1, 2, 3, kinda 5, 6, 7.

Mattuck is an excellent book available for very cheap. Assumes only Calculus 1. No video lectures and no solutions mean it's hard to teach off of.

Real Analysis 1 at Harvey Mudd -- has 1, 2, 4, 5, 6.

The analysis course currently linked in the OSSU Math curriculum. Honestly, Prof. Su seems to support his class well and may make Rudin palatable for the first-timer, but I'm skeptical.

Several courses assigning homework out of Abbott's text, often regarded as a good first choice text, but without videos or solutions

I'd like to find some video lectures of a competent professor teaching out of Abbott, that would be about perfect for this course.

Adapt Abbott to the Bill Kinney Bethel lectures and cobble a complete course together

A concept I had. Abbott appears to follow this course pretty well, read chapters 1, 2, 3, 4, 5, 7, 6, 8. Can't guarantee coverage of topics but it seems to be fairly close by.

Just teach yourself out of Book Of Proof and Mattuck/Abbott

The current state of things, but I think we can do better.

I checked EdX and Coursera, and they seem to be fresh out of real analysis.

So, a few things I'd like us to consider:

• How does OSSU feel about recommending a course with a required textbook that isn't readily available? The library is an option
• Am I even focusing on the right ideals?
• Am I correct in assuming a course in baby Rudin is "too advanced" for a first analysis class (for mere mortals who didn't get into Harvey Mudd)? Does Prof. Su redeem the difficulty?
• Has anybody taken any of these or others, and has other courses to recommend?
• Is there a good course in Advanced/Honors Calculus/Intro Analysis that's using Spivak's Calculus text? I haven't investigated this. Maybe that presents a better option. (Feel free to slap me if that's definitely not a better option.)
• What other resources are out there that I haven't seen yet? Links, links, links, links! :)

And finally, the big takeaway:

I think from what I've seen so far, the Intro to Real Analysis at Bethel is the closest thing we have to the right first analysis course. In order for me to feel good about recommending it, we need to host the documents somewhere that isn't a Google Drive. I don't really know the best way to go about doing that (except perhaps by making a Github Pages site for the course).

Replace missing Differential Equation courses

Problem:

• The curriculum links to several Differential Equation courses that are no longer offered.

Duration:
Oct 31

Background:
The fall out from edX going for profit continues. Three differential equations courses have been removed from edX and do not appear to have been recreated on MITx:

• Differential Equations: Linear Algebra and NxN Systems of Differential Equations
• Differential Equations: Fourier Series and Partial Differential Equations
• Differential Equations: Fourier Series and Partial Differential Equations
  View a Wayback Capture of the previous edX Diff EQ series.

Proposal:
Replace all of these courses with the MIT OCW Scholar version of Differential Equations.

Alternatives:
Offerings of note:

• System Functions and the Laplace Transform: Does this course cover the material of the 3rd course that was removed?
• Differential Equations for Engineers from The Hong Kong University of Science and Technology on Coursera
• Three course Differential Equations series from Korea Advanced Institute of Science and Technology(KAIST) on Coursera. One and two and three.
• Two part ODE and Linear Algebra course from Rice on edX. One and two.
• Differential Equations and Linear Algebra: This is listed as Supplemental Resources on MIT OCW.
• Differential Equations For Engineers from IITM
• Fan favorite: Professor Leonard

MATLAB

Can we add matlab training courses as it is synonymous with statistics, graphing, solving complex equations and is just something nice to learn :) ?

Repo Needs a License File

Not sure what the best license choice, but we do need one for the OSSU mathematics program.

Definition of done:

• License file added to repo

Links Under Curriculum Should Lead to Sections Not Direct Courses

When clicking a link under the Curriculum Section, the user is taken to a specific course. Links should be updated to take user to that section.

Current Behavior: Clicking Introduction to Mathematical Thinking takes users directly to the Coursera course.
Desired Behavior: Clicking Introduction to Mathematical Thinking takes users to the Introduction to Mathematical Thinking section.

The course "Introduction to Differential Equations"

I tried to enter the course but EdX says "We can't seem to find the page you're looking for.", so I don't know if it is not available anymore.

Need for advanced analysis classes

There are quite a few texts on introductory analysis, but we should start looking at more advanced analysis classes to start filling the curriculum. We should probably look at introducing the Rudin books (Papa/Grandpa) and start searching for problem sets and videos. The UCCS videos may be very helpful here.