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Basic Mathematics

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Johnson, George; Laura Mansnerus (May 3, 1987). "Science Academy Rejects Harvard Political Scientist". New York Times . Retrieved August 13, 2010. Shakarchi, Rami (1996). Solutions manual for Lang's "Linear Algebra". New York: Springer-Verlag. doi: 10.1007/978-1-4612-0755-9. ISBN 0-387-94760-4. MR 1415837. Lang, Serge (1966). Introduction to transcendental numbers. Reading, MA–London–Don Mills, Ontario: Addison-Wesley Publishing Co. MR 0214547.

Basic Mathematics by Serge Lang | Waterstones

If you're exceptionally concerned about rigor, you can get the full story on the set-theoretical foundations of mathematics from a book like Introduction to Set Theory, by Jech and Hrbacek. This builds up from the axioms of set theory to a construction of the natural numbers, and later of the integers, rational numbers and real numbers. The problem is that while such a program is pre-Spivak in purely logical terms, it is post-Spivak in the demands it places on readers' mathematical maturity. For comparison, Spivak constructs the real numbers in the last part of his book, but he takes the rational numbers and their properties as intuitively known. My opinion is that few people would benefit from working through a set theory book before Spivak, but it may be helpful to have a general idea of what the steps are in providing a firm logical foundation for mathematics. Meacham, R. C. (1966-01-01). "Review of A Second Course in Calculus". Mathematics Magazine. 39 (2): 124. doi: 10.2307/2688730. JSTOR 2688730. Lang, Serge (1985). SL 2(R). Graduate Texts in Mathematics. Vol.105 (Reprint of the 1975 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4612-5142-2. ISBN 0-387-96198-4. MR 0803508. [21] a b Lang, Serge (1981). The File: Case Study in Correction (1977-1979). New York, NY: Springer New York. doi: 10.1007/978-1-4613-8145-7. ISBN 978-1-4613-8145-7 . Retrieved 4 May 2022. Libro di testo completo e interessante, scritto da un matematico davvero in gamba, che sa come veicolare concetti base e avanzati in maniera unica, tramite svariati esempi e diverse dimostrazioni.Hochschild, G. (1969). "Review: Rapport sur la cohomologie des groupes by Serge Lang" (PDF). Bull. Amer. Math. Soc. 75 (5): 927–929. doi: 10.1090/s0002-9904-1969-12294-9.

Algebraic Number Theory | SpringerLink Algebraic Number Theory | SpringerLink

Abraham, Ralph (1964). "Review: Introduction to differential manifolds. By Serge Lang" (PDF). Bull. Amer. Math. Soc. 70 (2): 225–227. doi: 10.1090/s0002-9904-1964-11089-2. Lang, Serge (2000). Collected papers. III. 1978–1990. Springer Collected Works in Mathematics. New York: Springer. ISBN 0-387-98800-9. MR 1781669. 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. Baker, Alan (1980). "Review: Elliptic curves: Diophantine analysis, by Serge Lang" (PDF). Bull. Amer. Math. Soc. (N.S.). 2 (2): 352–354. doi: 10.1090/s0273-0979-1980-14756-4. Lang, Serge (1983). Abelian varieties (Reprint of 1959 originaled.). New York–Berlin: Springer-Verlag. doi: 10.1007/978-1-4419-8534-7. ISBN 0-387-90875-7. MR 0713430.urn:oclc:record:1357510392 Foldoutcount 0 Identifier basicmathematics0000lang Identifier-ark ark:/13960/s28bdx3fm2s Invoice 1652 Isbn 0387967877 Lccn 88012334 Ocr tesseract 5.2.0-1-gc42a Ocr_detected_lang en Ocr_detected_lang_conf 1.0000 Ocr_detected_script Latin Ocr_detected_script_conf 0.9433 Ocr_module_version 0.0.18 Ocr_parameters -l eng Old_pallet IA-WL-1300189 Openlibrary_edition Jorgenson, Jay; Lang, Serge (1993). Basic Analysis of Regularized Series and Products. Lecture Notes in Mathematics. Vol.1564. Berlin: Springer-Verlag. doi: 10.1007/BFb0077194. ISBN 3-540-57488-3. MR 1284924. Lang, Serge (1986). Introduction to linear algebra. Undergraduate Texts in Mathematics (Second edition of 1970 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4612-1070-2. ISBN 978-0-387-96205-4. S2CID 117514050. Fortunatamente ci sono molte soluzioni agli esercizi alla fine del libro, così da poter rivedere il proprio lavoro e avere eventuali conferme. Serge Lang was an influential mathematician in the field of number theory. Algebra is his most famous book.

Basic Mathematics by Serge Lang | Goodreads

Jorgenson, Jay; Lang, Serge (2008). The heat kernel and theta inversion on SL 2(C). Springer Monographs in Mathematics. New York: Springer. doi: 10.1007/978-0-387-38032-2. ISBN 978-0-387-38031-5. MR 2449649. Lang, Serge (1999). Complex analysis. Graduate Texts in Mathematics. Vol.103 (Fourth edition of 1977 originaled.). New York: Springer-Verlag. doi: 10.1007/978-1-4757-3083-8. ISBN 0-387-98592-1. MR 1659317. 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 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. Jorgenson, Jay; Krantz, Steven G., eds. (April 2007). "The Mathematical Contributions of Serge Lang" (PDF). Notices of the AMS. 54 (4): 476–497.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’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 Langlands, R. P. (1976). " SL 2(R), by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (5): 688–691. doi: 10.1090/s0002-9904-1976-14109-2. But these are minor quibbles. On the whole, Lang compares well to most books at a similar level. If you don't want to wait for calculus to dot all the i's and cross all the t's, you could read The Real Number System by Olmsted in parallel. Lang, Serge (2005). Undergraduate algebra. Undergraduate Texts in Mathematics (Third edition of 1990 originaled.). New York: Springer-Verlag. doi: 10.1007/0-387-27475-8. ISBN 0-387-22025-9. The 1990 first edition was itself a second edition of Algebraic Structures (1967)

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