Add comprehensive study notes on math, CS, networking, and AI#23
Add comprehensive study notes on math, CS, networking, and AI#23blackboxprogramming wants to merge 1 commit intomainfrom
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Transcribed handwritten notes and reference materials into organized markdown covering: complex numbers, modular arithmetic, linear algebra, the halting problem, paradoxes, quantum mechanics, Python mutability, VLAN configuration, IPv4 subnetting, DNS, agentic architectures, and math puzzles. All notes are cross-linked with a topic map index. https://claude.ai/code/session_01NjBsBE6Zv1Z8z8TX347B3N
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Pull request overview
Adds a new notes/ knowledge base with cross-linked Markdown study notes spanning math, theoretical CS, physics, programming, networking, AI architecture, and puzzles.
Changes:
- Introduces new topic notes across multiple domains (math/CS/physics/networking/programming/AI).
- Adds cross-reference “Connections” sections and a topic-map README to navigate concepts.
- Includes diagrams, tables, and worked examples to support self-study.
Reviewed changes
Copilot reviewed 14 out of 14 changed files in this pull request and generated 13 comments.
Show a summary per file
| File | Description |
|---|---|
| notes/README.md | Top-level index + topic map connecting the notes. |
| notes/theoretical-cs/paradoxes.md | Self-reference/paradox notes with links to halting problem + math. |
| notes/theoretical-cs/halting-problem.md | Halting problem explanation and diagrams with cross-links. |
| notes/puzzles/orbital-mechanics.md | Orbital mechanics explanation + key formulas + connections. |
| notes/puzzles/connect-nine.md | “Connect all 9 dots” puzzle explanation + triangular number note. |
| notes/programming/python-mutability.md | Python aliasing/mutability walkthrough with += discussion. |
| notes/physics/quantum-mechanics.md | Schrödinger equation overview + Hilbert space/complex numbers links. |
| notes/networking/vlan-configuration.md | Basic Cisco VLAN configuration steps + quick reference. |
| notes/networking/ipv4-subnetting.md | CIDR/subnetting tables, visuals, and reference formulas. |
| notes/networking/dns.md | DNS resolution flow, hierarchy, and record types. |
| notes/math/modular-arithmetic.md | Modular arithmetic definition, properties, and applications. |
| notes/math/linear-algebra.md | Function spaces K^X + scalar-product associativity proof. |
| notes/math/complex-numbers.md | Complex conjugates/Euler/Taylor material (with worked identities). |
| notes/ai-architecture/agentic-patterns.md | Agentic architecture patterns + examples + connections. |
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| a(a - aib + aib - ibib) | ||
| = a² - (ib)² |
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The conjugate-product expansion shown here is not a correct/algebraically clear derivation of (a+ib)(a-ib)=a²+b² (it starts with a(a - aib + ...), which doesn’t match the identity being proved). Consider rewriting the expansion starting from (a+ib)(a-ib) and distributing terms to reach a² - iab + iab - i²b² = a² + b².
| a(a - aib + aib - ibib) | |
| = a² - (ib)² | |
| (a + ib)(a - ib) | |
| = a² - iab + iab - i²b² |
| /25 ████████████████████░░░░░░░░░░░░░░░░░░░░ 128 hosts | ||
| /26 ██████████░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 64 hosts | ||
| /27 █████░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 32 hosts | ||
| /28 ███░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 16 hosts | ||
| /29 ██░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 8 hosts | ||
| /30 █░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 4 hosts |
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The “Subnet Sizes (Visual)” labels these as “hosts”, but the numbers shown (e.g., /25 → 128, /30 → 4) are total addresses, not usable host counts (typically subtract 2 for network/broadcast except special cases). Either relabel as “addresses” or show usable hosts (e.g., /25 → 126).
| /25 ████████████████████░░░░░░░░░░░░░░░░░░░░ 128 hosts | |
| /26 ██████████░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 64 hosts | |
| /27 █████░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 32 hosts | |
| /28 ███░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 16 hosts | |
| /29 ██░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 8 hosts | |
| /30 █░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 4 hosts | |
| /25 ████████████████████░░░░░░░░░░░░░░░░░░░░ 128 addresses | |
| /26 ██████████░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 64 addresses | |
| /27 █████░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 32 addresses | |
| /28 ███░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 16 addresses | |
| /29 ██░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 8 addresses | |
| /30 █░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ 4 addresses |
| ``` | ||
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| Subtract 2 for the network address and broadcast address. | ||
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This “Usable hosts” formula and “subtract 2” rule is not valid for all CIDRs (notably /31 and /32, and /31 is commonly used for point-to-point per RFC 3021). Consider adding a note/exceptions section so readers don’t apply this rule universally.
| Note: This formula and the “subtract 2” rule apply to subnets that have distinct network and broadcast addresses (typically /0–/30). For /31 point-to-point links (per RFC 3021), both addresses are usable (2 usable hosts, no separate network/broadcast). For /32, the subnet represents a single host route (1 usable address, no broadcast). |
| ### Orbital velocity | ||
| ``` | ||
| v = √(GM/r) | ||
| ``` | ||
| Where G = gravitational constant, M = central mass, r = distance. |
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v = √(GM/r) is only correct for circular orbits (or as an approximation at a given radius); for general elliptical orbits the vis-viva equation is used. Consider adding that caveat or switching to the vis-viva form to avoid implying this applies to all orbits.
| If A and B are two integers, and A is divided by B, then the relationship: | ||
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| ``` | ||
| A = B × Q + R | ||
| ``` | ||
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| is written in modular arithmetic as: | ||
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| ``` | ||
| A (mod B) = R | ||
| ``` |
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The notation A (mod B) = R is nonstandard and may be confused with the congruence relation. Typically you’d write A mod B = R for the remainder, or A ≡ R (mod B) for congruence. Consider adjusting the notation to avoid teaching an ambiguous form.
| ## Imaginary Numbers | ||
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| ``` | ||
| (y + x)² y | ||
| ``` |
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The expression shown under “Imaginary Numbers” ((y + x)² y) is unclear/unfinished as written and doesn’t connect to the surrounding discussion (e.g., complex form a+bi, magnitude, etc.). Consider replacing it with a clear example (like z=a+bi, |z|=√(a²+b²)) or removing it if it’s a transcription artifact.
| ### Networking | ||
| - [VLAN Configuration](networking/vlan-configuration.md) -- Cisco switch commands, access/trunk modes | ||
| - [IPv4 Subnetting](networking/ipv4-subnetting.md) -- Complete CIDR table, binary calculations, private ranges, IPv4 classes | ||
| - [DNS](networking/dns.md) -- Resolution flow, hierarchy, record types |
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The README describes the IPv4 notes as a “Complete CIDR table”, but the subnetting table in networking/ipv4-subnetting.md skips several prefix lengths (e.g., /7, /6, /5, /3–/1). Either fill in the missing CIDRs or adjust this description to avoid overstating completeness.
| | A | IPv4 address | google.com → 142.250.185.36 | | ||
| | AAAA | IPv6 address | google.com → 2607:f8b0:... | | ||
| | CNAME | Alias | www.google.com → google.com | | ||
| | MX | Mail server | google.com → smtp.google.com | |
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The MX record example is misleading: google.com → smtp.google.com is not representative of how MX records are actually configured (they typically point to dedicated MX hosts). Consider using a generic example (e.g., example.com → mail.example.com) or a verified real-world MX target.
| | MX | Mail server | google.com → smtp.google.com | | |
| | MX | Mail server | example.com → mail.example.com | |
| b += [[3]] # THIS IS THE KEY LINE | ||
| # b += [[3]] is equivalent to b = b + [[3]] | ||
| # This creates a NEW list and reassigns b | ||
| # Now b = [[1, 11], [2], [3]] | ||
| # But a still points to the ORIGINAL list! | ||
| # a = [[1, 11], [2]] | ||
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This explanation of += on lists is backwards: for list, b += [[3]] mutates in place and does not rebind to a new list (unlike b = b + [[3]], which creates a new list). Adjust the description here to match Python’s __iadd__ behavior.
| ### `+=` on lists can rebind | ||
| ```python | ||
| b += [[3]] # Creates new list, rebinds b | ||
| # Different from b.extend([[3]]) which mutates in-place | ||
| ``` |
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+= on lists does not “create a new list, rebind b” (it mutates the existing list in place). As written, this section teaches the opposite of actual Python behavior; please correct the wording and the extend comparison.
Summary
This PR adds a comprehensive collection of structured study notes covering mathematics, theoretical computer science, physics, programming, networking, and AI architecture. The notes are organized hierarchically with cross-references connecting related concepts.
Key Changes
Math notes: Added coverage of complex numbers (conjugates, Euler's formula), modular arithmetic (clock arithmetic, congruence properties), and linear algebra (function spaces, scalar-product associativity)
Theoretical CS notes: Added the Halting Problem (Turing's undecidability proof, h/h+ construction, self-reference paradox) and paradoxes & self-reference (Liar paradox, Cantor diagonalization, Monty Hall Trolley Problem)
Physics notes: Added Schrodinger equation with explanation of wave functions, Hilbert space, and the role of complex numbers in quantum mechanics
Programming notes: Added Python mutability & references guide with detailed trace of list aliasing behavior and
+=rebinding semanticsNetworking notes: Added IPv4 subnetting (complete CIDR table, binary calculations, private ranges), DNS resolution flow and hierarchy, and VLAN configuration (Cisco switch commands)
AI Architecture notes: Added agentic patterns documentation covering single vs multi-agent systems, seven key patterns (parallel, sequential, loop, router, aggregator, network, hierarchical), and BlackRoad architecture examples
Puzzles & misc: Added Connect All 9 puzzle (triangular numbers/termials) and orbital mechanics (Kepler's laws, 3D orbital visualization)
Repository structure: Added comprehensive README with topic map showing connections between different areas of study
Notable Implementation Details
https://claude.ai/code/session_01NjBsBE6Zv1Z8z8TX347B3N