1. Vectors and Matrices

2. Matrix Operations and Properties

3. Dot Product and Cross Product

4. Matrix Inverse, Transpose, Determinant

5. Eigenvalues and Eigenvectors

6. Linear Transformations

7. Singular Value Decomposition (SVD)

8. Principal Component Analysis (PCA)

Probability and Statistics (Core to Inference, Predictions, and Modeling) 

1. Descriptive Statistics: Mean, Median, Mode, Variance, Standard Deviation

2. Probability Theory: Conditional Probability, Bayes’ Theorem

3. Random Variables and Probability Distributions (Bernoulli, Binomial, Poisson, Normal, etc.)

4. Expectation and Variance

5. Law of Large Numbers and Central Limit Theorem

6. Hypothesis Testing and p-values

7. Confidence Intervals

8. Statistical Inference

9. Correlation and Covariance

Optimization (For Model Training and Resource Allocation) 

1. Convex vs. Non-convex Functions

2. Lagrange Multipliers

3. Linear Programming and Integer Programming

4. Quadratic Programming

5. Stochastic Optimization

Mathematical Foundations for Machine Learning 

1. Functions, Limits, and Continuity

2. Derivatives and Gradients

3. Partial Derivatives and Jacobians

4. Chain Rule

5. Optimization: Minima and Maxima

6. Gradient Descent and its Variants

7. Multivariable Calculus (for deep learning)

Discrete Mathematics (Important for Algorithms and Data Structures) 

1. Set Theory and Logic

2. Combinatorics and Counting

3. Graph Theory (used in network analysis)

4. Recursion and Induction

5. Relations and Functions

Information Theory (Used in Data Compression, Decision Trees, Deep Learning) 

1. Entropy

2. Information Gain

3. Kullback-Leibler Divergence

4. Mutual Information

Time Series and Signal Processing (For Temporal Data Analysis) 

1. Stationarity

2. Autocorrelation and Partial Autocorrelation

3. AR, MA, ARIMA Models

4. Fourier and Laplace Transforms (Advanced)

Additional Topics 

1. Numerical Methods (for computational solutions)

2. Dimensionality Reduction Techniques

3. Matrix Factorization (for recommendation systems)

4. Markov Chains (for modeling state transitions)

5. Bayesian Inference (for probabilistic modeling)

Geometry and Vector Spaces (For Feature Engineering and Deep Learning)