Lang was a prolific writer of mathematical texts, often completing one on his summer vacation. Most are at the graduate level. He wrote calculus texts and also prepared a book on group cohomology for Bourbaki. Lang's Algebra, a graduate-level introduction to abstract algebra, was a highly influential text that ran through numerous updated editions. His Steele prize citation stated, "Lang's Algebra changed the way graduate algebra is taught...It has affected all subsequent graduate-level algebra books." It contained ideas of his teacher, Artin; some of the most interesting passages in Algebraic Number Theory also reflect Artin's influence and ideas that might otherwise not have been published in that or any form. Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. Vol.211 (Revised third edition of 1965 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4613-0041-0. ISBN 0-387-95385-X. MR 1878556. Questions of Scientific Responsibility: The Baltimore Case From the journal Ethics and Behavior Vol. 3 No. 1 (1993) pp. 3–72, Serge Lang, Mathematics Department, Yale University

Basic Mathematics by Serge Lang - Physics Forums Basic Mathematics by Serge Lang - Physics Forums

Jorgenson, Jay; Lang, Serge (2001). Spherical inversion on SL n(R). Springer Monographs in Mathematics. New York: Springer-Verlag. doi: 10.1007/978-1-4684-9302-3. ISBN 0-387-95115-6. MR 1834111. [29] The basic topics covered doesn't necessarily mean that the book will be easy; this was my first introduction to proofs, and to trying to create my own (which I often failed at doing). However, even if I knew most of the material already (like that a negative number multiplied by a negative number results in a positive number), I had never known the reasoning behind why this was true. The logical approach presented taught me a different, more effective way to learn mathematics. Lang even has an entire section (somewhere after chapter 3, I think) where he simply covers logic and some notation, to help the reader get a better grasp of the idea.Lang, Serge (1987). Calculus of several variables. Undergraduate Texts in Mathematics (Third edition of 1973 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4612-1068-9. ISBN 978-0-387-96405-8. Originally published as A Second Course in Calculus (1965) [14] [15] [16]

Basic Mathematics by Serge Lang | Goodreads Basic Mathematics by Serge Lang | Goodreads

L’unica pecca sono gli esercizi proposti che, nonostante la maggior parte siano davvero interessanti e stimolanti, a volte risultano troppo complicati e non in linea con i capitoli e gli argomenti appena studiati, rendendo alcuni passaggi del libro frustranti e noiosi. Lang’s Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books."—NOTICES OF THE AMS Lang, Serge (1994). Algebraic number theory. Graduate Texts in Mathematics. Vol.110 (Second edition of 1970 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4612-0853-2. ISBN 0-387-94225-4. MR 1282723. [25] The first edition was itself the second edition of Algebraic Numbers (1964)

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Lang, Serge (1987). Elliptic functions. Graduate Texts in Mathematics. Vol.112. With an appendix by J. Tate (Second edition of 1973 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4612-4752-4. ISBN 0-387-96508-4. MR 0890960. [22] Lang, Serge; Murrow, Gene (1988). Geometry: a high school course. New York: Springer-Verlag. doi: 10.1007/978-1-4757-2022-8. ISBN 978-0-387-96654-0. From April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books: "Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." Part (2) is important, and I agree that Lang's book is short on this topic. But the trigonometry and complex number chapters of Parsonson's Pure Mathematics 1 and 2 (which I mentioned to you previously) ought to be quite enough for this. It's not necessary that this be taken beyond the level of Lang before you study calculus. Serge Lang (18 May 1978), "The Professors: A Survey of a Survey", The New York Review of Books available online as reprinted in Challenges