Intereting Posts

showing Cohen-Macaulay property is preserved under a ring extension
Limit of sums of iid random variables which are not square-integrable
Combinatorial proof that $\frac{({10!})!}{{10!}^{9!}}$ is an integer
Is $L^{p}$ space with alternate norm banach?
Negation of uniform convergence
$G/H$ is a finite group so $G\cong\mathbb Z$
Prove that $ \int \limits_a^b f(x) dx$ = $ \int \limits_a^b f(a+b-x) dx$
How can I prove the identity $2(n-1)n^{n-2}=\sum_k\binom{n}{k}k^{k-1}(n-k)^{n-k-1}$?
Global sections on quasi coherent sheaves on affine scheme
product of two uniformly continuous functions is uniformly continuous
How to derive the expected value of even powers of a standard normal random variable?
Continuous linear image of closed, bounded, and convex set of a Hilbert Space is compact
Are there always at least $3$ integers $x$ where $an < x \le an+n$ and $\gcd(x,\frac{n}{4}\#)=1$
How to explain to a 14-year-old that $\sqrt{(-3)^2}$ isn't $-3$?
Give an example of a non-separable subspace of a separable space

I currently have the book Dynamical Systems with Applications Using Mathematica by Stephen Lynch. I used it in an undergrad introductory course for dynamical systems, but it’s extremely terse. As an example, one section of the book dropped the term ‘manifold’ at one point without giving a definition for the term. This is only one example; the rest of the book is similarly sparse on information.

I have a background in applied mathematics and computer science. If it’s necessary to cover some pre-requisite topics to get a good grasp of the subject (eg, topology, abstract algebra, etc), please feel free to mention this.

I’d love it if there were some pre-recorded lectures on the topic, but I’m not holding my breath. I’m looking for a book satisfying the following:

- Suggest books in calculus to improve problem solving skills
- Stochastic calculus book recommendation
- Resources/Books for Discrete Mathematics
- Introductory text for lattice theory
- What are good books to learn graph theory?
- Deducing formulas of analytic geometry

- Needs to be readable without PhD level experience, for
*self study* - Should cover both continuous and discrete dynamical systems
- Bifurcation theory, lyapunov functions, manifolds, etc
- My goal is to be able to understand more advanced treatments of the topic, but I don’t have an immense amount of free time. Among my frustrations with studying this particular topic is the material is so dense I spend a great deal of time trying to decipher terse phrases that turn out to be rather straightforward, just written cryptically.

- Proofs in Linear Algebra via Topology
- How does Dummit and Foote's abstract algebra text compare to others?
- Books for starting with analysis
- what are prerequisite to study Stochastic differential geometry?
- Any good Graduate Level linear algebra textbook for practice/problem solving?
- Good Textbooks for Real Analysis and Topology.
- Textbook for Partial Differential Equations with a viewpoint towards Geometry.
- Lyapunov Stability of Non-autonomous Nonlinear Dynamical Systems
- Book recommendation to prepare for geometry in the International Mathematical Olympiad
- Good books for self-studying algebra?

*Nonlinear Dynamics and Chaos* by Steven Strogatz is a great introductory text for dynamical systems. The writing style is somewhat informal, and the perspective is very “applied.” It includes topics from bifurcation theory, continuous and discrete dynamical systems, Liapunov functions, etc. and is very readable.

If you’re looking for something a little more advanced, some suggestions would be *Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations* by Paul Glendinning or *Introduction to Applied Nonlinear Dynamical Systems and Chaos* by Stephen Wiggins. These two texts include all of the topics above, along with much more discussion about manifolds and their stability.

The gratest mathematical book I have ever read happen to be on the topic of discrete dynamical systems and this is A “First Course in Discrete Dynamical Systems” Holmgren. This books is so easy to read that it feels like very light and extremly interesting novel. Topics introduced by Holmgren made me see mathematics in entirely new light and be happy as a child when he discover something new.

“An Introduction to Chaotic Dynamical Systems” is the one I prefer

- How to prove this inequality $\frac{x^y}{y^x}+\frac{y^z}{z^y}+\frac{z^x}{x^z}\ge 3$
- Tensors constructed out of metric other than the Riemann curvature tensor
- If $d$ is a metric, then $d/(1+d)$ is also a metric
- Exponential Function as an Infinite Product
- Why are clopen sets a union of connected components?
- Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?
- Characteristic subgroups of a direct product of groups
- Why is $\zeta(2) = \frac{\pi^2}{6}$ almost equal to $\sqrt{e}$?
- derivation of derangement with inclusion -exclusion
- Proving Nonhomogeneous ODE is Bounded
- Finding the sum of $\sin(0^\circ) + \sin(1^\circ) + \sin(2^\circ) + \cdots +\sin(180^\circ)$
- How many ways are there to divide $100$ different balls into $5$ different boxes so the last $2$ boxes contains even number of balls?
- Simple example of non-arithmetic ring
- $\mathbb{R}^3$ \ $\mathbb{Q}^3$ is union of disjoint lines. The lines are not in an axis diretion.
- Which universities teach true infinitesimal calculus?