JulianGrossmann_Math.txt

# DR. JULIAN P. GROSSMANN - Mathematician

## No.:
## Title:
## https links: 


1.
DR. JULIAN P. GROSSMANN personal webpage 
https://jp-g.de


https://jp-g.de/teaching2/



Linear Algebra 
20th July 2022, Version 2.4
https://jp-g.de/Skripte/LA-GES-CS-JPG.pdf

https://jp-g.de/post/ws18-lae/



Real Analysis 
20th July 2022, Version 2.4
https://jp-g.de/Skripte/RA-JPG.pdf

https://youtube.com/playlist?list=PLBh2i93oe2quABbNq4I_-hyjhW8eOdgrO



Measure Theory 
https://youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j



Probability Theory 
https://youtube.com/playlist?list=PLBh2i93oe2qswFOC98oSFc37-0f4S3D4z



Distributions 
https://www.youtube.com/playlist?list=PLBh2i93oe2qsbptdcvFlowCl51EX_a3nB



2.
Markdown Syntax 
https://markdown.tw



3.
Metrics math real analysis
https://www.startpage.com/sp/search



3-1
Metric (mathematics)
https://en.wikipedia.org/wiki/Metric_(mathematics)



3-2
Real Analysis: Metric Spaces - Paul Skoufranis
https://pskoufra.info.yorku.ca/files/2019/12/M4011-LectureNotes.pdf?x25477



3-3

http://alpha.math.uga.edu/~usher/notes.pdf



3-4
Real Analysis on Metric Spaces - Mark Dean
http://www.columbia.edu/~md3405/Maths_RA1_14.pdf



3-5
8.1: Metric Spaces - Jiří Lebl (Oklahoma State University)
https://math.libretexts.org/Bookshelves/Analysis/Introduction_to_Real_Analysis_(Lebl)/08:_Metric_Spaces/8.01:_Metric_Spaces



3-6
Metric and Topological Spaces - Definition and examples of metric spaces
http://www-groups.mcs.st-andrews.ac.uk/~john/MT4522/Lectures/L5.html



3-7
Definition of a metric
https://math.stackexchange.com/questions/319759/definition-of-a-metric



3-8
Introduction to Real Analysis - Fall 2014 Lecture Notes - Vern I. Paulsen
https://www.math.uh.edu/~vern/4331lec.pdf



3-9
Metric Spaces
https://math.okstate.edu/people/lebl/uw521-f11/mspaces.pdf



3-10
Metric Spaces
https://www.geneseo.edu/~aguilar/public/notes/Real-Analysis-HTML/ch9-metric-spaces.html



3-11
Is it helpful to teach about metric spaces in a first real analysis course?
https://www.quora.com/Is-it-helpful-to-teach-about-metric-spaces-in-a-first-real-analysis-course

Not really.

Metric spaces is more of a specific set up for things like measure theory, and acts, in my opinion at least, as a framework for defining points and distances in sets, as well as the sets themselves.

All results from Real Analysis can be formulated from the perspective of metric spaces, but to do so in a first course would introduce a student to too much unnecessary machinery at once, disguising the motivation behind analysis.

The definitions in real analysis would barely change. In fact, they would be abstracted away from the reals into any set on which there exists a metric. To some of the uninitiated this sounds like a dream; learn a general method for analysis in any measurable set. But as someone who has taken both courses I can safely say you need to learn to walk before you can run.

Once the framework of metric spaces is introduced AFTER all the real analysis, it is much more straightforward for a student to take it all in and generalise to measurable sets- primarily because it's effectively a second pass of all the information from real analysis, just abstracting those basic notions to any measurable set you like.



4.
Basic Analysis: Introduction to Real Analysis - By: Jiří Lebl
email: jiri.lebl@gmail.com

https://github.com/jirilebl/ra

https://www.jirka.org/ra/

Download the volume I of the book as PDF
https://www.jirka.org/ra/realanal.pdf
(Version 5.6, May 16th, 2022, 282 pages, 1.8 MB download)

Download the volume II of the book as PDF
https://www.jirka.org/ra/realanal2.pdf
(Version 2.6, May 16th, 2022, 195 pages, 1.4 MB download)

Check for any errata (volume I) (volume II) in the current version.
https://www.jirka.org/ra/errata.html

https://www.jirka.org/ra/errata2.html

Look at the change log (volume I) (volume II) to see what changed in the newest version.

https://www.jirka.org/ra/changes.html

https://www.jirka.org/ra/changes2.html

I started numbering things with version numbers starting at 4.0 for volume I, and version 1.0 for volume II. The first number is the major number and it really means "edition" and will be raised when substantial changes are made. The second number is raised for corrections only.



5.
Real Analysis 
https://www.geneseo.edu/~aguilar/


An Introduction to Real Analysis by Cesar Aguilar
https://www.geneseo.edu/~aguilar/public/assets/courses/324/real-analysis-cesar-aguilar.pdf


Real Analysis I MATH 324 : Spring 2022
https://www.geneseo.edu/~aguilar/courses/math/324


Real Analysis II MATH 325 : Spring 2022
https://www.geneseo.edu/~aguilar/courses/math/325


An Introduction to Real Analysis
https://www.geneseo.edu/~aguilar/public/notes/Real-Analysis-HTML/index.html


Calculus II
https://www.geneseo.edu/~aguilar/public/notes/Calculus-2-HTML/index.html

3. Sequences and Series
https://www.geneseo.edu/~aguilar/public/notes/Calculus-2-HTML/ch3-sequences-and-series.html



6.
Calculus with Julia notes
https://jverzani.github.io/CalculusWithJuliaNotes.jl/

https://github.com/jverzani/CalculusWithJuliaNotes.jl

https://github.com/jverzani/CalculusWithJulia.jl


https://jverzani.github.io/CalculusWithJuliaNotes.jl/limits/limits.html

https://jverzani.github.io/CalculusWithJuliaNotes.jl/derivatives/symbolic_derivatives.html

https://jverzani.github.io/CalculusWithJuliaNotes.jl/derivatives/optimization.html

https://jverzani.github.io/CalculusWithJuliaNotes.jl/derivatives/newtons_method.html

https://jverzani.github.io/CalculusWithJuliaNotes.jl/derivatives/lhospitals_rule.html

https://jverzani.github.io/CalculusWithJuliaNotes.jl/derivatives/taylor_series_polynomials.html


Julia in the classroom
https://julialang.org/learning/classes/