Little Bits of Artificial Intelligence

1. Basic Math Knowledge for Understanding Traditional Machine Learning

1. Arithmetic & Algebra

• What We Need to Know:
  • Basic operations: +, -, ×, ÷
  • Solving simple equations
  • Using variables (x, y, w, etc.)
• Why It’s Needed:
  • Most models (like linear regression) are just equations using weights and features.

2. Functions & Graphs

• What We Need to Know:
  • Understanding y = f(x) format
  • Plotting straight lines and curves
  • Knowing slope, intercept, increasing/decreasing
• Why It’s Needed:
  • ML models are functions that map input to output. Visualizing them helps grasp what’s happening.

3. Statistics & Probability (Basics)

• What We Need to Know:
  • Mean (average), Median, Mode
  • Variance and Standard Deviation (spread of data)
  • Probability basics: chance of something happening
• Why It’s Needed:
  • Many models evaluate uncertainty or patterns in data (e.g., Naive Bayes, Logistic Regression).

4. Linear Algebra (Intro Level)

• What We Need to Know:
  • Vectors: like [x1, x2, x3]
  • Matrix basics: tables of numbers, rows × columns
  • Matrix multiplication (conceptually)
• Why It’s Needed:
  • Data and weights are often represented in vector/matrix form.

5. Coordinate Geometry (Basics)

• What We Need to Know:
  • 2D plane: x and y axes
  • Distance between two points
• Why It’s Needed:
  • Helps understand concepts like decision boundaries, nearest neighbors, etc.

6. Optimization Concept (Very Light)

• What We Need to Know:
  • Finding the best value (like minimizing error)
  • Understand idea of “adjusting” parameters
• Why It’s Needed:
  • ML models learn by minimizing errors — we don’t need calculus, just the idea of “tuning to improve”.

2. Basic Math Knowledge for Understanding Deep Learning

1. Arithmetic & Algebra

• Already needed for traditional ML
• What We Need to Know:
  • Working with equations, unknowns (x, w, b)
  • Rearranging terms, solving for variables

In Deep Learning: We’ll see formulas like:

y = w1*x1 + w2*x2 + … + b repeated many times, layer by layer.

2. Functions & Activation Functions

• What We Need to Know:
  • What functions do: take input → give output
  • Concept of non-linear functions: squashing or bending values
• Example Functions:
  • Sigmoid (S-curve)
  • ReLU (like a ramp: 0 if negative, value if positive)

In Deep Learning: Activation functions decide if a neuron “fires” or not.

3. Matrices & Vectors (Linear Algebra – Light)

• What We Need to Know:
  • Vector = list of numbers ([x1, x2, x3])
  • Matrix = table of numbers
  • Dot product = pairwise multiply and add

In Deep Learning: Inputs, weights, and outputs are all stored as vectors/matrices. Most computations are matrix multiplications.

4. Basic Probability & Statistics

• What We Need to Know:
  • Mean, variance, standard deviation
  • Probability basics (chance, likelihood)

In Deep Learning: Often used in:

• Dropout (randomly turning off neurons)
• Loss functions like cross-entropy
• Output interpretation (e.g., classification probabilities)

5. Basic Calculus (Conceptual)

• What We Need to Know:
  • Derivatives tell us how something is changing
  • Gradient = direction of fastest change
  • We do not need to compute them by hand

In Deep Learning:

• Used in backpropagation to update weights (learning from error)
• Just knowing the idea of minimizing error by changing weights is enough at first

6. Optimization Concepts

• What We Need to Know:
  • Trial-and-error to improve results
  • Gradient Descent = step-by-step learning
  • Learning rate = how big each step is

In Deep Learning: Training is just finding the best weights to reduce error.