Intereting Posts

Calculate half life of esters
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
The two distinct cultures in mathematics
A semicontinuous function discontinuous at an uncountable number of points?
Let $F_\infty=\bigcup_{n\geq1}\operatorname{Q}(2^{1/2^n})$ , $K_\infty=\bigcup_{n\geq1}\operatorname{Q}(\zeta_{2^n})$, what is the intersection?
Existence of $\{\omega, \omega+1,…\}$ via the axiom of replacement
Greatest common divisor in the Gaussian Integers
A special subgroup of groups of order $n$
The square of minimum area with three vertices on a parabola
what is the$ \int \sin (x^2) \, dx$?
About the strictly convexity of log-sum-exp function
Proving there are no subfields
show that $\det(A)=0$ in this case
Common factors of cyclotomic polynomials and polynomials with prime coefficients
Prove that the sequence $(n+2)/(3n^2 – 1)$ converges to the limit $0$

I’m studying Brannan’s *Geometry* and Lang’s *Introduction to Linear Algebra* and I was wondering if there are some exercise books (that is, books with ** solved** problems and exercises) that I can use as companions.

The books I’m searching for should be:

- full of
*hard*,*non-obvious*,*non-common*, and*thought-provoking*problems; - rich of
*complete*,*step by step*,*rigorous*, and*enlightening*solutions.

- What is a good book to study linear algebra?
- (Theoretical) Multivariable Calculus Textbooks
- Good way to learn Ramsey Theory
- What is a good book for learning math from the ground up?
- book for metric spaces
- What is a good book for learning Stochastic Calculus?

- How to graph in hyperbolic geometry?
- Simple proof that equilateral triangles have maximum area
- How many sides does a circle have?
- Find equation of a plane throw two given point and orthogonal to another space
- Find the parametric form $S(u, v)$ where $a \le u \le b$ and $c \le v \le d$ for the triangle with vertices $(1, 1, 1), (4, 2, 1),$ and $(1, 2, 2)$.
- Equation of Cone vs Elliptic Paraboloid
- Resources/Books for Discrete Mathematics
- Lines cutting regions
- Best book ever on Number Theory
- Looking for a (nonlinear) map from $n$-dimensional cube to an $n$-dimensional simplex

A classic in linear algebra is Paul R. Halmos’ Linear Algebra Problem Book.

In fact it’s also a great book teaching many aspects of linear algebra and a great book in teaching

how to solve problems. The first part contains more than 160 problems, the last part contains detailed solutions. A nice idea is a small chapter in between about 15 pages long, which containshintsfor each of the problems.

The reader is encouraged even if he is able to solve a problem to also check the solution, since they may contain additional info in form of interesting comments.

I fully agree with the end of his preface:

I hope you will enjoy trying to solve problems.

I hope you will learn something by doing so, and I hope you will have fun.

Let me start by mentioning a series of books on linear algebra, by T. S. Blyth and E. F. Robertson, that I consider to be really enlightening:

*Theory + Solved Exercises*

- Basic Linear Algebra
- Further Linear Algebra

*Solved Exercises*

- Algebra Through Practice: Volume 2, Matrices and Vector Spaces
- Algebra Through Practice: Volume 4, Linear Algebra

And now, my secret weapons (more directed towards matrix theory):

- Matrix Algebra, by K. Abadir and J. Magnus;
- Problems and Solutions in Introductory and Advanced Matrix Calculus, by Willi-Hans Steeb.

Have fun!

I agree with Timbuc, the Schaum’s calculus book has helped me with having many solved problems and explanations. I have seen a geometry addition being sold on amazon and ebay for a pretty good price

I’ve studied on this. Actually it’s in Italian but it’s a wonderful text.

- Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z…: unified treatment of transforms?
- Prove that for any nonnegative integer n the number $5^{5^{n+1}} + 5^{5 ^n} + 1$ is not prime
- Unique representation of a vector
- For a function from $\mathbb{R}$ to itself whose graph is connected in $\mathbb{R} \times \mathbb{R}$, yet is not continuous
- Partial Fractions Expansion of $\tanh(z)/z$
- Number of permutations which are products of exactly two disjoint cycles.
- Reference request for algebraic Peter-Weyl theorem?
- Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
- Explain Zermelo–Fraenkel set theory in layman terms
- How to rotate n individuals at a dinner party so that every guest meets every other guests
- Volume of spheres in higher dimensions?
- Fixed point iteration convergence of $\sin(x)$ in Java
- Can a relation with less than 3 elements be considered transitive?
- How to show that $(a+b)^p\le 2^p (a^p+b^p)$
- converse to the jordan curve theorem