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02. Academics 📚
02.00. archived
discreteMath
Lec 01 - Set Theory
*** discreteMathLec01 map
cardinality
equal set
MATH2020 (Lec 01) - Set Theory
ordered n-tuples
power set
set definition
set operations
strings
subset
Lec 02 - Proof Techniques
*** discreteMathLec02 map
Direct proof
Indirect proof
Non-constructive proof of existence
Proof by cases and examples
Proof by contradiction
Proof by contrapositive
proof technique term definition
Lec 03 - Functions and Relations
*** discreteMath Lec 03 Map
bijection
functions
injection
rational and irrational numbers
relations
set cardinality
set countability
surjection
Lec 04 - Induction, Strong Induction
*** discreteMath Lec 04 map
induction principle
strong induction principle
Lec 05 - Well Ordering Principle
*** discreteMath Lec 05 map
Fermat's Last Theorem for n = 3, 4
Infinite descent principle
Well ordering principle
Lec 06 - Divisibility and GCD
*** discreteMath Lec 06 map
Divisibility
Euclid & GCD algorithm
Extended Euclidean algorithm
Greatest common divisor
Number theory
Lec 07 - Modular Arithmetic
*** discreteMath Lec 07 map
Addition modulo operation
Arithmetic modulo
Commutative group
Congruent modulo
Hashing
Modular arithmetic
Multiplication modulo
Lec 08 - Prime Numbers
*** discreteMath Lec 08 map
Primality test
Prime number
Lec 09 - The Euler Function
*** discreteMath Lec 09 map
Chinese remainder theorem
Euler function
Euler's theorem
Fermat's little theorem
Lec 10+11 - Cryptography
*** discreteMath Lec 10+11 map
caesar cipher
cryptography
private key encryption scheme
Lec 12 - Introduction to Graphs
*** discreteMath Lec 12 map
Complete Graph
Directed graph
Edge
Graph
Graph representation
Tree
Undirected graph
Vertex
Lec 13 - graph isomorphism
*** discreteMath Lec 13 map
Bipartite Graph
Cycle
Euler Cycle
Euler Path
Graph isomorphism
Hamilton Cycle
Hamilton Path
Path
Lec 14 - Graph Euler and Hamiltonian Path
*** discreteMath Lec 14 map
Matching
Lec 15 - Planar Graph and Coloring
*** discreteMath Lec 15 map
Chromatic Number
Graph Coloring
Planar Graph
Lec 16 - Intro to Automata
*** discreteMath Lec 16 map
Automata Theory
Deterministic Finite-state Automata
Finite State Machine
Nondeterministic Finite-state Automata (NFA)
MATH2020 (Lec 02) - Proof Techniques
MATH2020 (Lec 03) - Functions and Relations
MATH2020 (Lec 04) - Induction, Strong Induction
MATH2020 (Lec 05) - Well Ordering Principle
MATH2020 (Lec 06) - Divisibility and GCD
MATH2020 (Lec 07) - Modular Arithmetic
MATH2020 (Lec 08) - Prime Numbers
MATH2020 (Lec 09) - The Euler Function
MATH2020 (Lec 10) - Cryptography
MATH2020 (Lec 11) -
MATH2020 (Lec 12) - Introduction to Graphs
note for cheatsheet
linearAlgebra
Lec 2
*** lec 2 topics remained
*** linear2 map
affine
basis
determinant
dimension
euclidean length, vector length
linear combination
linear independence
orthogonal AND orthonormal
relations between vector space, span, subspace, affine set, hyperplane
scalar product AND euclidean inner product OR dot product
subspace and span
vector distance, euclidean distance
Vector space
Vectors & Unit vectors
Lec 3
first order taylor approximation
gradient
hyperplanes & halfspaces
linear transformation OR functions and maps
Lec 4
***
cauchy-schwart inequality
norms and lp norms
RMS (root mean square) value
sample average
Lec 5
complex scalar product
fourier basis
gram-schmidt process
orthonormal basis
projection of the span on orthonormal vectors
projection on a line
Lec 6
***
cross product
low rank matrix
matrices as linear maps
matrix basics
matrix matrix product
matrix vector product
Lec 7
fundamental theorem of linear algebra
inference in LA
matrix inverse
null space
range AND rank
trace AND determinant
Lec 8 + 9
***special case of QR
eigenvectors AND eigenvalues
Google's Page Rank
QR decomposition
similar matrices
use eigenvectors as basis - eigenbasis
Lec 18
*** linearLec18 map
Dyads
Matrix properties via SVD
singular values
SVD
Lec 19
*** linearLec19 map
low rank approximation
low rank matrix approximations
low rank models and projections
cheat sheet
least squares method
microEcon
archived
ECON1010 (Lec 01) - 10 principles of microecon
ECON1010 (Lec 02) - Thinking Like an Economist
ECON1010 (Lec 03) - Interdependence and the Gains from Trade
ECON1010 (Lec 04) - The Market Forces of Supply and Demand
ECON1010 (Lec 05) - Elasticity and Its Applications
ECON1010 (Lec 06) - Supply, Demand, and Government Policies
ECON1010 (Lec 07) - Consumers, Producers, and the Efficiency of Markets
ECON1010 (Lec 08) - Application, The Costs of Taxation
group asm - evn case
lec 01 - 10 principles of microecon
*** microEcon lec 1 map
10 principles of microecon
definition of economy vs economics
Governments Can Sometimes Improve Market Outcomes (principle 7 _ microecons)
Markets Are Usually a Good Way to Organize Economic Activity
people face tradeoffs (principle 1 _ microecons)
People Respond to Incentives (principle 4 _ microecons)
Prices Rise Too Much When the Government Prints Too Much Money
Rational People Think at the Margin (principle 3 _ microecons)
Society Faces a Short-run Tradeoff Between Inflation and Unemployment
The Cost of Something Is What You Give Up to Get It (principle 2 _ microecons)
The Standard of Living Depends on a Country's Production
Trade Can Make Everyone Better Off (principle 5 _ microecons)
lec 14 - perfect competition
*** lec 14 - perfect competition (microEcon Map)
firm and industry - equilibrium price
market structure
perfect competition
perfect competition and efficiency
profit maximization in the long run
Profit Maximization Rule
short run output decision & short run supply curve
total revenue, average revenue, marginal revenue
lec 15 - monopoly
*** lec 15 - monopoly (microEcon map)
causes of monopoly
deadweight loss
efficient level of output
Increasing Competition with Antitrust Laws
monopoly firm definition
monopoly revenue
Monopoly vs Competition
Price Discrimination in Monopolies
profit calculation
profit maximization in monopoly
Public Ownership of Monopolies
public policy toward monopolies
regulation of monopolies
types of monopoly
lec 16 - oligopoly
lec 16 - oligopoly
lec 13 - cost production
lec 17 - Monopolistic Competition
02.01. templateCourse
*** templateCourse map
AY2S2
AI
*** AI map
a* search
breadth-first search - bfs
cost-sensitive search
definition of an agent
depth-first search - dfs
designing rational agents
fringe strategy - the one queue
greedy search
iterative deepening
learning agents
models
options to design an AI agent
pancake problem
planning agent
reflex agent
search algorithm
search heuristics
search problems
search tree
state space
state space graph
state space graph vs search tree
the different approached to AI
the importance of AI
the structure of agents
tree search algorithm
uniform cost search - ucs
what is AI
algoDesign
*** algoDesign map
algorithm design process
Gale Shapley Algorithm
stable matching problem
time complexity & space complexity
comOrg
*** comOrg map
2-to-1 MUX
4-to-1 MUX
base10 - decimal, base2 - binary, base16 - hexadecimal
cmos notation
Combinational circuits
decoder
encoder
equality comparators using XOR
hide complexity in logic gates through abstraction
instruction set architecture (ISA)
logic gates
logic implementation _ from truth tables to logic circuits
logic symbols & notation
moore's law
multiplexer - MUX
negative numbers _ sign-magnitude + twos-complement + sign extension & truncation
transistors _ n-type and p-type
translators - assembler + compiler + interpreter
universal gates _ nand + nor
history2
*** history 2 map
Có cần phải cải tiến chữ quốc ngữ?
đường sắt bắc nam
his2lec2 questions
Nhật Bản
probStat
*** chapters reflection
prob stat chapters reflection
AY2.03. probStat
02 - bayes theorem, conditional prob
03 - Conditional Probability and Independence
04 - Sampling and Data
05 - Descriptive Statistics
06 - Discrete Random Variables
07 - Continuous Random Variables
09 - Properties of Expectation
10 - Limit Theorems
11 - Interval Estimation
12 - Hypothesis Test
Background Info on Limit Theorems
Central Limit Theorem
Conditional Probability, Product Rule, Independent Events, Bayes Theorem
correlation between confidence level & width of interval
Forms for Null and Alternative Hypothesis
Hypothesis Test on Population mean
Independent Variables Inference (Expectation, Var, Std)
Inequalities
Level of Significance
p-value
Practical Interpretation of Limit Theorems
Sampling and Data General Info
Sampling Methods
Survey Methods
Test claim using a confidence interval (a, b)
The Strong Law of Large Numbers
The Weak Law of Large Numbers
Type 1 and Type 2 errors & Consequence
Types of Data Collection
Untitled
Chapter 1
Combination
Permutation
Population
Population mean
Sample mean
Chapter 2
Bayes theorem
Combinatorial analysis
Conditional probability
Intersect operation
Mutually exclusive
Probability
Probability mass function
Sample space
Statistical event
Union operation
Chapter 3
Standard deviation
Chapter 4
Non-response error
Response error
Sample
Sampling and data
Sampling error
Chapter 5
Descriptive statistic
Chapter 6
Binomial distribution
Cumulative distribution function
Discrete random variable
Expected value
Poisson distribution
Skewness
Sum of independent variables
Systematic sampling
Variance
Chapter 7
Continuous random variable
Distribution of a function of a random variable
Exponential distribution
Gamma distribution
Hazard rate function
Normal distribution
Probability density function
Standard normal distribution
The DeMoivre-Laplace limit theorem
Uniform distribution
Chapter 8
Chi-squared distribution
Conditional joint distribution
Independent random variable
Joint cumulative distribution function
Joint distribution of functions of variables
Joint probability density function
Joint probability mass function
Jointly distributed random variable
Marginal probability mass function
Chapter 9
Conditional expectation
Conditional variance
Correlation
Covariance
Linear regression
Moment generating function
Properties of expectation
Regression Model
Sample variance
Chapter 10
Central limit theorem
Chebyshev's inequality
Distribution of sample mean
Indicator Variable
Law of large number
Limit theorems
Markov's inequality
Mean square error
Strong law of large numbers
Weak law of large numbers
Chapter 11
Confidence interval
Prediction
t distribution
Chapter 12
Alternative Hypothesis
Hypothesis Testing
Null Hypothesis
Type 1 Error
Type 2 Error
Chapter 13
Difference random variable of 2 variables
*** probStat Map
MATH2010
probStatAdvanced
*** probStatAdvanced Map
Simple Linear Regression Model
selfLearn
AI-agentWithAutoGen
Agent - From links to lessons
Ideas - Ideas on creating agents
javascript
javascript fundamental scrimba course
largeLanguageModels
large language model (LLM)
machineLearning
Fundamental of Machine Learning
Machine Learning
Supervised Learning
Unsupervised Learning
startup
*** startup map
*** Academics Map
Home
❯
02. Academics 📚
❯
02.00. archived
❯
linearAlgebra
❯
Lec 5
❯
complex scalar product
complex scalar product
Mar 10, 2024, 1 min read
Hermitian scalar product
definition
x
H
y
=
∑
i
=
1
n
x
i
y
i
ˉ
, where if
y
=
a
+
bi
then
y
ˉ
=
a
−
bi
Graph View
Table of Contents
Hermitian scalar product
definition
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