The Big Naughty List

General

• Search Engines/AI: ChatGPT, Bing -Copilot-, Claude 3 and Meta AI -they are still not available in many countries-, perplexity, Poe, SearXNG (it is an open-source metasearch engine), DuckDuckGo, Gemini, and Google.

  In DuckDuckGo, the exclamation mark ("!") is referred to as a “bang.” It allows you to perform searches on specific websites directly from the DuckDuckGo search bar, e.g., !g (Google), !w (Wikipedia), !yt (YouTube).

• Ollama allows you to run Llama2, Code Llama and other models.

  user@pc:~$ ollama run llama2
  user@pc:~$ A circle has the radius 5. What is the area of the circle?
  The area of a circle can be calculated using the formula: Area =πr², where r is the radius of the circle. In this case, the radius of the circle is 5, so the area of the circle is: Area = π(5)² = 3.14(5²) = 78.5
  
  So the area of the circle is 78.5 square units.
  

• Wolfram|Alpha.
• Alternatives
• Pr∞fWiki is an online compendium of mathematical proofs.
• Mathematics Stacks Exchange is a question and answer site for people studying math at any level and professionals in related fields.
• Problems in Mathematics, problems and their solutions/proofs in mathematics.
• Wualoah un lugar donde compartir apuntes, exámenes y otros recursos.
• Video sharing: YouTube, Internet Archive, D.tube, and odysee.
• Varios: Online Matplotlib Compiler, Cheatography.

Super useful

• 12ft Clean any webpage.
• Have I been pwned Check if your email address is in a data breach.

Biography General

1. Mathematics LibreTexts.
2. Khan Academy.
3. Evan Dummit’s Course Notes Page.

Video Lectures

1. Free Video Lectures, All Courses, Mathematics.
2. Andrew Misseldine.
3. ICTP Mathematics, Abstract Algebra - Lothar Göttsche
4. Oxford Mathematics, 1st Year Student Lectures.
5. MIT OpenCourseWare, MIT 18.01 Single Variable Calculus, Fall 2007.
6. Richard E. BORCHERDS.
7. A First Course in Calculus.

Math symbols

• Greek letters, α, β, γ, δ, ε, ζ, η, θ, ι, λ, μ, π
• ∀ ∃ ≈ ∞
• ℕ ℤ ℝ ℂ ∉ ∅ # {} [] @
• < , >, ≤, ≥, ≠.
• ×, ÷, ±, ∓, 7·8
• ∪, ∩, ⊆, ⊂, ⊊, ⊃, ∈, ∉, ∅
• →, ←, ⇒, ⇐, ↦, ⟹ , ⟺
• HTML Symbols, Entities, Characters, and Codes and HTML Symbols.

Latex

• LaTeX/Mathematics
• List of LaTeX mathematical symbols
• In order to use math, enclose your formulae with dollar signs “$”. You can also use so-called displaymath blocks by using two dollar signs.
• Special symbols and notations, e.g., \lt \gt \le \ge \neq, $\lt \gt \le \ge \neq$
• \times \div \pm \mp 7\cdot9: $\times \div \pm \mp 7\cdot9$
• \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing: $\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing$
• \to \gets \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto \implies \iff: $\to \gets \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto \implies \iff $
• \forall \exists \approx \infty: $\forall \exists \approx \infty$
• {n+1 \choose 2k}: ${n+1 \choose 2k}$
• Square root: \sqrt{2}, $\sqrt{2}$
• Square n: \sqrt[n]{2}, $\sqrt[n]{2}$
• Limit: \lim_{x \to 0} f(x), \lim_{\Delta x \to 0} \frac{f(x_0+\Delta x) -f(x_0)}{\Delta x} ⇨ $\lim_{x \to 0} f(x)$, $\lim_{\Delta x \to 0} \frac{f(x_0+\Delta x) -f(x_0)}{\Delta x}$
• Fractions: \frac{2}{3}, $\frac{2}{3}$
• Superscripts and subscripts, e.g., 2^{3}, x_0: $2^{3}, x_0$
• \frac{d}{du}e^{u}|_{u=0}, $\frac{d}{du}e^{u}|_{u=0}$
• Sums and integrals, e.g., \sum_{i=0}^\infty i, \int x^{n}: $\sum_{i=0}^\infty i, \int x^{n}$
• Whitespace: \frac{d}{dx} lnx|_ {x=1}=~1, $\frac{d}{dx} lnx|_ {x=1}=~1$
• Greek letters: \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \lambda, \mu, $\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \lambda, \mu$
• Symbols, e.g., \Delta x, \epsilon, \pm: $\Delta x, \epsilon, \pm $.
• Matrix. GL(2, ℝ) = \bigl\\{ {{[\bigl(\begin{smallmatrix}a & b\\\ c & d\end{smallmatrix}\bigr)]: a, b, c, d ∈ ℝ, ad - bc ≠ 0}} \bigr\}: $GL(2, ℝ) = \bigl\{ {{[\bigl(\begin{smallmatrix}a & b\\ c & d\end{smallmatrix}\bigr)]: a, b, c, d ∈ ℝ, ad - bc ≠ 0}} \bigr\}$
• Embedding text, e.g., \text{In a different notation}, $\text{In a different notation}$.

Software

• The best Maths software to learn and grow: Speedcrunch, Microsoft Mathematics, Microsoft Math Solver, Maxima, JFractionLab, Gnuplot, GeoGebra, LibreOffice & OpenOffice Calc, Numerical Chameleon, Octave, and R.
• Kids: Gcompris, Omnitux, The KDE Education Project, Tux of Math Command, Kitsune, and TuxMathScrablle.

Calculus

1. Calculus Early Transcendentals
2. MTH 210 Calculus I (Professor Dean))
3. UTRGV Calculus
4. Study Guides, Calculus.
5. Paul’s Online Notes, QUICK NAV, Calculus I.
6. Math24, Calculus.
7. Calculus, 4ed. Michael Spivak.

Algebra

• Mathonline, and more specifically, Abstract Algebra.
• Abstract Algebra: Theory and Applications.
• Andrew Misseldine: College Algebra and Abstract Algebra.
• Michael Penn (Abstract Algebra), and MathMajor
• Lectures by Benedict Gross, Abstract Algebra
• LibreTexts Mathematics, Bookshelves, Abstract and Geometric Algebra, Abstract Algebra: Theory and Applications (Judson). Calculus and Calculus 3e (Apex).
• Course Notes - J.S. Milne Top. All of Milne’s books are really kind and very easy to read (math.stackexchange.com).
• Contemporary Abstract Algebra, Joseph, A. Gallian.
• A First Course in Abstract Algebra, John Fraleigh.
• Abstract Algebra, 3ed. David S. Dummit. Richard M. Foote.
• Topics in Algebra” by Herstein

Topology

• Marius Furter (Topology).
• Introduction to Topological Manifolds. John M. Lee. Available in Internet Archive.
• MAT327 at the University of Toronto Online Notes with Problems: MAT327 Course Note

Linear Algebra

• Andrew Misseldine, Linear Algebra Done Openly.
• Linear Algebra Done Right by Sheldon Axler & Videos: Sheldon Axler’s Playlist.
• GeoGebra 3D Calculator
• MyWhyU, Algebra.
• Linear Algebra Done Openly is an open source linear algebra textbook developed by Dr. Andrew Misseldine
• Online Python
• LibreTexts Mathematics, Bookshelves, Advanced Algebra.

College Algebra

• Andrew Misseldine, College Algebra.

Galois Theory

1. NPTEL-NOC IITM, Introduction to Galois Theory.
2. Algebra, Second Edition, by Michael Artin.
3. Galois theory (2ed, London, 1944) by Dr. Emil Artin. Lectures delivered at the University of Notre Dame.
4. Richard E. BORCHERDS, Galois Theory.
5. Notes by Tom Leinster
6. Evan Dummit’s Course Notes Page, Fields and Galois Theory, Fall 2020.

Complex Analysis

• Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert
• Complex Analysis” by Serge Lang
• Videos: Wesleyan University Playlist (Actually unavailable)

Algebraic Topology

• Book: Algebraic Topology by Allen Hatcher
• Lectures by Pierre Albin

YouTube Channels

• Socratica.
• The Math Sorcerer.
• Kimberly Brehm.
• Numberphile.
• Eddie Woo.
• patrickJMT.
• blackpenredpen.
• math Antics.
• Stand-up Maths.
• Professor Leonard.
• 3Blue1Brown.
• blackpenredpen
• The Organic Chemistry Tutor.
• A Mathematical Room.
• Chau Tu.

YouTube Math Visual

• Mathemaniac
• Aleph 0
• Infinity Learn Class 9&10.
• The Bright Side of Mathematics.