Serge lang Definition and 13 Threads

I have encountered this theorem in Serge Lang's linear algebra: Theorem 3.1. Let F: V --> W be a linear map whose kernel is {O}, then If v1 , ... ,vn are linearly independent elements of V, then F(v1), ... ,F(vn) are linearly independent elements of W. In the proof he starts with C1F(v1) +...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > Hello. I'm currently working my way through Lang's Basic Mathematics and cannot make sense of this question: Show that if n is a positive integer at most equal to m, then {m \choose n}+{m\choose...

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

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...

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

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"...

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...

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...