Collection of Free Online Math Books and Lecture Notes (part 1)

In summary: PVB/Harrison/MathforPhysicists.pdf “Tensor calculus for physics”http://www.iucaa.in/~puri/mtp/tensors.pdf In summary, students looking for affordable textbooks in mathematics and mathematical physics can find a variety of resources available for free online. These textbooks cover a wide range of topics, including introductory mathematics, calculus, real analysis, linear algebra, differential equations, complex analysis, abstract algebra, topology, measure theory, functional analysis, and differential geometry/mathematical physics. These resources include both pre-prints of published books and online resources that can be downloaded or read online. With the abundance of these free resources, students can save money and still have
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malawi_glenn
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School starts soon, and I know students are looking to get their textbooks at bargain prices đŸ€‘

Inspired by this thread I thought that I could share some of my findings of 100% legally free textbooks and lecture notes in mathematics and mathematical physics (mostly focused on geometry) (some of these are pre-prints of published books) (some you can download as a pdf, some you have to read online)đŸ“šđŸ–„ïž

There are many many more out there, and I have for sure not read all of the ones in this post. If you have read any of these, or have other suggestions, feel free to share it in this thread :smile: (The ones that I have read, I will write about at some point).

Note: I have not included video lecture series, or interactive sites, only stuff you can read like a textbook.

I might do another thread in the future for physics books... :atom:🌟

Anyway, here you go, enjoy 🎁


Calculus and Real analysis

“Calculus Volume 1, 2, 3 (Openstax)”

https://assets.openstax.org/oscms-prodcms/media/documents/CalculusVolume1-OP.pdf
more info https://openstax.org/details/books/calculus-volume-1
https://assets.openstax.org/oscms-prodcms/media/documents/CalculusVolume2-OP.pdf
more info https://openstax.org/details/books/calculus-volume-2
https://assets.openstax.org/oscms-prodcms/media/documents/CalculusVolume3-OP.pdf
more info https://openstax.org/details/books/calculus-volume-3

“Calculus Volume 1, 2, 3 (Paul’s online notes)”
https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
https://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx
https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx
more info https://tutorial.math.lamar.edu/

“Introduction to real analysis”
http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF
more info http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml

“Basic analysis: Introduction to real analysis”
Volume 1: https://www.jirka.org/ra/realanal.pdf
Volume 2: https://www.jirka.org/ra/realanal2.pdf
more info https://www.jirka.org/ra/

“Real analysis”
http://mathonline.wikidot.com/real-analysis

“Vector calculus for Engineers”
https://www.math.hkust.edu.hk/~machas/vector-calculus-for-engineers.pdf
Even though the title says “for engineers” the stuff should be pretty good for for pure math and physics too!

“Vector calculus (Corral)”
https://math.libretexts.org/Bookshelves/Calculus/Book:_Vector_Calculus_(Corral)

“CLP Calculus textbooks”
https://personal.math.ubc.ca/~CLP/

Linear Algebra

“A first course in linear algebra (Kuttler)”

https://batch.libretexts.org/print/Finished/math-14495/Full.pdf
more info math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)

“A first course in linear algebra (Beezer)”
http://linear.pugetsound.edu/download/fcla-3.50-tablet.pdf
more info http://linear.pugetsound.edu/

“Linear algebra (Hefferon)”
https://joshua.smcvt.edu/linearalgebra/book.pdf
more info https://joshua.smcvt.edu/linearalgebra/

“Linear algebra with applications (Nicholson)”
https://lila1.lyryx.com/textbooks/OPEN_LAWA_1/marketing/Nicholson-OpenLAWA-2021A.pdf
more info https://lyryx.com/linear-algebra-applications/

“Linear algebra done wrong”
https://www.math.brown.edu/streil/papers/LADW/LADW_2017-09-04.pdf
more info https://www.math.brown.edu/streil/papers/LADW/LADW.html
Do not let the title discourage you. It is a hint to a very good and popular linear algebra book called “Linear Algebra done right” by Sheldon Axler. In that book, the author avoids the usage of determinants as much as possible.

“Linear algebra (Math online)”
http://mathonline.wikidot.com/linear-algebra

“Introduction to Matrix algebra”
http://autarkaw.com/books/matrixalgebra/index.html

Differential equations

“Notes of Diffy Qs: Differential equations for engineers”
https://www.jirka.org/diffyqs/diffyqs.pdf
more info https://www.jirka.org/diffyqs/
Even though the title says “for engineers” the stuff should be pretty good for for pure math and physics too!

“Differential equations (Paul’s online notes)”
https://tutorial.math.lamar.edu/Classes/DE/DE.aspx

“Elementary differential equations”
https://digitalcommons.trinity.edu/cgi/viewcontent.cgi?article=1007&context=mono

“Differential equations (Math online)”
http://mathonline.wikidot.com/differential-equations

"Ordinary Differential Equations and Dynamical Systems (Teschl)"
https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf
more info https://www.mat.univie.ac.at/~gerald/ftp/book-ode/

Complex analysis

“A first course in complex analysis”

http://math.sfsu.edu/beck/papers/complexorth.pdf
more info https://matthbeck.github.io/complex.html

“Guide to Cultivating Complex Analysis - Working the Complex Field”
https://www.jirka.org/ca/ca.pdf
more info https://www.jirka.org/ca/

“Complex analysis”
http://mathonline.wikidot.com/complex-analysis



Measure theory and integration

“Measure, Integration & Real Analysis”

https://measure.axler.net/MIRA.pdf
more info https://measure.axler.net/

“An introduction to measure theory”
https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf
more info https://terrytao.wordpress.com/books/an-introduction-to-measure-theory/

“Measure theory”
http://mathonline.wikidot.com/measure-theory

Functional analysis

“Lectures on functional analysis”

http://facultymembers.sbu.ac.ir/shahrokhi/HasseOpeThe.pdf

“Introduction to functional analysis (Daners)”
https://www.maths.usyd.edu.au/u/athomas/FunctionalAnalysis/daners-functional-analysis-2017.pdf

“Introduction to functional analysis (Kisil)”
http://www1.maths.leeds.ac.uk/~kisilv/courses/math3263m.pdf

“Functional analysis”
http://mathonline.wikidot.com/functional-analysis

Differential geometry/ Mathematical Physics

“Differential geometry in physics”
http://people.uncw.edu/lugo/COURSES/DiffGeom/DG1.pdf
more info http://people.uncw.edu/lugo/COURSES/DiffGeom/index.htm

“Quick introduction to tensor analysis”
https://arxiv.org/pdf/math/0403252.pdf

“A geometrical approach to differential forms”
https://maths.dur.ac.uk/users/mark.a.powell/Bachman_Geometric_Approach_to_Differential_Forms.pdf

“A simple introduction to particle physics part II”
https://arxiv.org/pdf/0908.1395.pdf
part I is also worth to check out

“Mathematics for Physics: An illustrated handbook”
https://www.mathphysicsbook.com/intro/
 
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Let there be known that links are valid as of 14_08_2022 and „link rots” are to be reported here, hopefully with the new valid links of the same documents/resources.
 
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Robert Ash has made books available for free download. I am only familiar with his basic probability book.
 
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  • #4
MidgetDwarf said:
Robert Ash has made books available for free download. I am only familiar with his basic probability book.
Yeah I had one of his included in the OP, I have his "Real Variables with Basic Metric Space Topology" on my Read-list (gonna check it out after I am done with Axlers book on real analysis).

Anyway, here they are:

Mathbooks by Robert Ash:

“Abstract algebra: the graduate year”
Included in the OP

"A course in algebraic number theory"

https://faculty.math.illinois.edu/~r-ash/ANT.html

"A course in commutative algebra"
https://faculty.math.illinois.edu/~r-ash/ComAlg.html

"Complex variables" (graduate course)
https://faculty.math.illinois.edu/~r-ash/CV.html

"Lectures on statistics"
https://faculty.math.illinois.edu/~r-ash/Stat.html

"Basic Probability theory"
https://faculty.math.illinois.edu/~r-ash/BPT.html

"Real Variables with Basic Metric Space Topology"
https://faculty.math.illinois.edu/~r-ash/RV.html

More info: https://faculty.math.illinois.edu/~r-ash/ Lecture notes by Robert Ash:

"Differential equations"

https://faculty.math.illinois.edu/~ash/DE.html

"Linear Algebra"
https://faculty.math.illinois.edu/~ash/LinearAlg.html

"Discrete Math"
https://faculty.math.illinois.edu/~ash/Discrete.html

"Advanced Calculus"
https://faculty.math.illinois.edu/~ash/AdvCalc.html

More info: https://faculty.math.illinois.edu/~ash/
 
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I wanted to refresh my algebra skills. I'm about halfway through abstract algebra - the basic graduate year, and recommend it.
 
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