# What is Lang: Definition and 35 Discussions

A hundred is a geographic division formerly used in northern Germanic countries and related colonies, which historically was used to divide a larger region into smaller administrative divisions. The equivalent term in Swedish is härad (in Uppland also known as hundare during the early Middle Ages); in Danish and Norwegian, herred; in Finnish, kihlakunta; and in Estonian, kihelkond.

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1. ### Is there a reason Lang uses (x-s)^2 instead of (x+s)^2?

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...
2. ### MHB Algebraic Closure of Fp [Lang, Algebra, Chapter 6, Problem 22]

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...
3. ### How Do You Calculate BMI in C Programming?

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: "...
4. ### Algebra Algebra: Lang vs Bourbaki Comparison

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.
5. ### Serge Lang as undergraduate algebra text

Good day, Did anyone here use Serge Lang's "Algebra" as an undergraduate text?
6. ### Algebra Dummit and Foote vs Lang: Choosing the Best Abstract Algebra Book

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...
7. ### Serge Lang: Increasing/Decreasing Function

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...
8. ### Calculus Serge Lang vs Larson & Edwards (Calculus)

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...
9. ### Serge Lang: Inequality Problem

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...
10. ### Linear Algebra Which Linear Algebra Book is Best for Self-Study: A Comparison of Lang and Axler

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...
11. ### I Have both books by Allendoerfer/Oakley do I need Lang?

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...
12. ### A first course in Calculus by Lang

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...
13. ### Study Calculus: Lang or Spivak?

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...
14. ### Lang or silverman or ?( intro calculus)

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...
15. ### Wish to help out in a research lab, which comp lang to learn?

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...

17. ### Geometry Is Geometry by Lang and Murrow Enough for a High School Course?

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...
18. ### Analysis Master Complex Analysis with Serge Lang: Prerequisites & Techniques for Grads

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...

21. ### Linear Algebra Introduction to Linear Algebra by Lang

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...
22. ### Calculus A First Course in Calculus by Lang

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...
23. ### Linear Algebra Linear Algebra by Serge Lang: Undergrad Theory & Applications

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...

25. ### Intro Math Is Basic Mathematics by Serge Lang the Right Math Book for You?

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...
26. ### Solutions Manual for Basic Mathematics by Serge Lang?

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...
27. ### A book to work along side 'Basic Mathematics' by Serge Lang

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
28. ### How to Count Characters and Words in a File Using C?

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:
29. ### Book similar to Basic Mathematics by Serge Lang

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"...
30. ### What do you think about Lang Textbooks?

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...
31. ### Ln vs. log in Short Calculus book by Serge Lang

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...
32. ### Show that (A:B) = (A^f:B^f)(A_f:B_f) in Abelian Groups

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...
33. ### Algebra Texts - Hungerford vs. Lang

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...
34. ### Computer circuits, assembly lang - from scratch

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...
35. ### Serge Lang multivariable calculus

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...