Lang Definition and 35 Threads

Homework Statement When learning about quadratic equations in Langs book he gave the example: let ax^2 + bx+ c = 0 be an equation he subtracts the c, and says we want to get the left hand side (ax^2 + bx) = (x-s)^2 Homework EquationsThe Attempt at a Solution I'm just interested, either my...

Problem. Let $K$ be the field obtained from $\mathbf F_p$ by adjoining all primitive $\ell$-th roots of unity for primes $\ell\neq p$. Then $K$ is algebraically closed. It suffices to show that the polynomial $x^{p^n}-x$ splits in $K$ for all $n$. In order to show this, it in turn suffices to...

Homework Statement Write a few lines of code that will accomplish the following: Ask the user to first enter his/her weight (in kilograms) and second enter the height (in meters). For every field to be filled in, print on screen the messages "Type your weight: " and "Type your height: "...

Hello, I have access to both Algebra (the graduate one) by Lang, and the series of Algebra Chapters 1-7 by the Bourbaki group. I am okay with Lang's style and all, and I am aware that he was in the Bourbaki group, but I was wondering what is considered the better of the two. Thanks in advance.

Good day, Did anyone here use Serge Lang's "Algebra" as an undergraduate text?

Hi, I'm going to start learning Abstract Algebra, and I was wondering which book, either Lang (his graduate version) or Dummit and Foote, is better. I'm totally okay with terseness to any degree so that isn't an issue for me. Now, I know that Lang is a hardcore graduate book (at least according...

Homework Statement Consider only values of ##x \geq 0##, and let ##f(x) = -x + \frac {x^3}{3!} + \sin x##. Show whether ##f## is increasing or decreasing. Homework Equations f(x) = -x + \frac {x^3}{3!} + \sin x f'(x) = -1 + \frac {x^2}{2} + \cos x The Attempt at a Solution I know that...

I have a copy of both Lang's text and Larson and Edwards' text, and was wondering which would be best for someone looking for a deeper understanding of Calculus. Any and all advice is welcome here! I was working through Kleppner & Kolenkow's Introduction to Mechanics and decided I need a much...

Hello, all. I am reading Serge Lang's "A First Course in Calculus" in order to get a better understanding of the topic. I thought I would read his review of fundamental concepts, and, naturally, it has been a breeze so far. However, I am stumped when trying to work out this problem: I do not...

I decide to self-study linear algebra. I have heard words about some good books on this subject such as Sheldon Axler's. Unfortunately his book is only loanable for 4 days in my university library. There is this book from S. Lang that I can borrow for one month, so what do you think about this...

I am starting my self-study and am going from the ground up starting with a rigorous treatment of some "pre-calculus" material. I have both "Principles of Mathematics" and "Freshman Mathematics" by Allendoerfer and Oakley. Do I need Serge Lang's Basic Mathematics? Is there anything that is...

I've noticed that the first edition has 250 some odd pages and I believe the last edition has over 500 pages. Would I be missing out on any material if I bought an earlier edition? I have a limited amount of time so the shorter the text the better. I also noticed it does not use Epsilon Delta...

I'm looking to begin an independent study of Calculus, having read Lang's Basic Mathematics. I would like to know if I should move straight on to Spivak's Calculus, or start with Lang's A First Course in Calculus? If it affects the answer in any way, I have had some rudimentary experience with...

I've just bought(and borrowed) these books : A first course in calculus by lang(621 pages but apparentely I've heard it lacks exercises(not enough)) Essential Calculus with Applications by silverman(286 pages apparently very good exercises) or The calculus lifesaver by Banner(about the same...

Hello I am a undergrad electrical engineering student. I took two courses on C before. With C, this seems to be not enough because I am hoping to help out in some engineering related research project at school. Currently, I have no idea what type of research I am looking for. I am just...

Author: Serge Lang Title: Fundamentals of Differential Geometry Amazon Link: https://www.amazon.com/dp/038798593X/?tag=pfamazon01-20 Prerequisities: Grad Analysis, Differential Geometry Level: Grad Table of Contents: Foreword Acknowledgments General Differential Theory Differential...

Author: Serge Lang and Gene Murrow Title: Geometry Amazon Link: https://www.amazon.com/dp/1441930841/?tag=pfamazon01-20 Prerequisities: High-school algebra Level: High school Table of Contents: Introduction Distance and Angles Lines Distance Angles Proofs Right Angles and...

Author: Serge Lang Title: Complex Analysis Amazon Link: https://www.amazon.com/dp/0387985921/?tag=pfamazon01-20 Prerequisities: Basic analysis Level: Grad Table of Contents: Foreword Prerequisites Basic Theory Complex Numbers and Functions Definition Polar Form Complex Valued...

Author: Serge Lang Title: Real and Functional Analysis by Lang Amazon Link: https://www.amazon.com/dp/0387940014/?tag=pfamazon01-20 Prerequisities: Undergrad analysis Level: Grad Table of Contents: General Topology Sets Some Basic Terminology Denumerable Sets Zorn's Lemma...

Author: Serge Lang Title: Undergraduate Analysis Amazon Link: https://www.amazon.com/dp/1441928537/?tag=pfamazon01-20 Prerequisities: Calculus, Proofs Level: Undergrad Table of Contents: Foreword Review of Calculus Sets and Mappings Sets Mappings Natural Numbers and Induction...

Author: Serge Lang Title: Introduction to Linear Algebra Amazon Link: https://www.amazon.com/dp/3540780602/?tag=pfamazon01-20 Prerequisities: High-School mathematics Level: Undergrad Table of Contents: Vectors Definition of Points in Space Located Vectors Scalar Product The Norm of...

Author: Serge Lang Title: A First Course in Calculus Amazon Link: https://www.amazon.com/dp/0387962018/?tag=pfamazon01-20 Prerequisities: High-school mathematics Level: Undergrad Table of Contents: Review of Basic Material Numbers and Functions Integers, rational numbers, and real...

Author: Serge Lang Title: Linear Algebra Amazon Link: https://www.amazon.com/dp/1441930817/?tag=pfamazon01-20 Prerequisities: Some familiarity with matrices and proofs Level: Undergrad Table of Contents: Basic Theory Vectors Definition of points in n-space Located vectors Scalar...

Author: Serge Lang Title: Algebra Amazon Link: https://www.amazon.com/dp/038795385X/?tag=pfamazon01-20 Prerequisities: Good knowledge of undergrad Algebra Level: Grad Table of Contents: The Basic Objects of Algebra Groups Monoids Groups Normal subgroups Cyclic groups Operations...

Author: Serge Lang Title: Basic Mathematics Amazon Link: https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20 Prerequisities: Mathematics before high school Level: Motivated high-school students, college students Contents: Real numbers, solving equations, logic, geometry, trigonometry...

I've been googling all over for a solutions manual to the book Basic Mathematics by Serge Lang, but I've only been able to find one for his book on geometry. It's not a terrible problem, but I'm using the book for self-study. At first it seemed that any exercise with multiple parts had at least...

Hey guys, the title basically says it all! I'm looking for a book to work along side Serge Lang's basic Math's book. Something which goes into topics more in depth. I'm out of scratch with my Math's :( Hope someone can point me to a good text! Luke

hi. please can anyone help me in making a program that opens a file and tell the no. of character and no. of words in the file. i can write a program to open a file but how can we count characters and words of any file..:confused:

Book similar to "Basic Mathematics by Serge Lang" I'm looking for a good book for my son, who wants to be a mathematician like me. He is totally into mathematics! Basically what I need is a "Apostol or Spivak for High School Math". What I mean is: I need a "rigorous mathematician's book"...

What do people think about Lang's textbooks? I am learning Complex Analysis for the first time from Lang. (literally the 1st time I'm seeing ANY sort of complex analysis/calculus, although I have extensive experience with real analysis). I have gone through quite a love-hate relationship with...

Homework Statement I've been going through a book called "Short Calculus: The Original Edition of A First Course in Calculus," by Serge Lang. It says, " The derivative of a^x is a^x (log a)." But everything else I look at says the derivative of a^x is a^x (ln a). Since ln a and log a are...

Let A and A' be abelian groups and B a subgroup of A. Let f: A -> A' be a group homomorphism. Let A^f = Im(f), B^f = Im(f|_B), A_f = Ker(f), B_f=Ker(f|_B) . Show that (A:B) = (A^f:B^f)(A_f:B_f) . This is the work I have done: We have B \subset E=f^{-1}(f(B)) . We also have an isomorphism...

Springer is having their annual Yellow Book sale and I was going to pick up an algebra text to supplement Dummitt and Foote. I'm not really satisfied with D&F--to me, the tone is too conversational and I have trouble finding the information I want from their long paragraphs of discussion...

I wish to design (if not actually build) an ultra-simple "computer" from scratch, just for fun and profit. I'm looking at only a fundamental level of computing power, with only one instruction, such as: "Given two single-digit numbers, output the product." I need three to design 3 things...

During my freshman year at Yale, I took a course in multivariable calculus under the tutelage of Prof. Serge Lang. He was also a fellow of my college, where I had the opportunity to dine with him. He was a very activated, no B. S. person whose life revolved around academics. I am honored to...