The following syllabus and objective statements are as per the latest PRM Guide.

**Note: **If an LOS is a link, that means the material for that LOS is available. The dates mentioned against each LOS is the date when the study material for that LOS is scheduled to arrive.

#### Foundations

- Describe Rules of algebraic operations
- List the Order of algebraic operations
- Characterize Sequences
- Characterize Series
- Characterize Exponents
- Characterize Logarithms
- Characterize Exponential function and Natural Logarithms
- Solve Linear equalities and inequalities in one unknown
- Demonstrate the Elimination method
- Demonstrate the Substitution method
- Solve Quadratic equations in one unknown
- Characterize Functions and Graphs
- Demonstrate continuous compounding
- Differentiate between discrete compounding and continuous compounding

#### Descriptive Statistics

- Describe various forms of Data
- Discuss Graphical representation of data
- Explain the concept of The Moments of a Distribution
- Define, Discuss and Calculate the Measures of Location or Central Tendency
- Define, Discuss and Calculate the Measures of Dispersion
- Calculate Historical Volatility from Returns Data
- Define, Discuss and Calculate Negative Semi-variance and Negative Semi-deviation
- Define, Discuss and Calculate Skewness
- Define, Discuss and Calculate Kurtosis
- Describe Bivariate Data
- Discuss Covariance and Covariance Matrix
- Discuss Correlation Coefficient and Correlation Matrix
- Calculate the volatility of a portfolio

#### Calculus

- Explain the concept of differentiation
- Demonstrate the application of the rules of differentiation to polynomial, exponential and logarithmic functions
- Calculate the modified duration of a bond
- Discuss Taylor Approximations
- Demonstrate the concept of convexity
- Demonstrate the concept of delta, gamma and vega
- Demonstrate Partial Differentiation
- Demonstrate Total Differentiation
- Discuss the Fundamental Theorem of Analysis
- List the Indefinite Integral(s) of function(s)
- Apply the Rules of Integration
- Discuss Optimisation of Univariate and Multivariate functions
- Demonstrate Constrained Optimisation using Lagrange Multipliers

#### Linear Mathematics and Matrix Algebra

- Demonstrate basic operations of Matrix Algebra
- Solve two Linear Simultaneous Equations using Matrix Algebra
- Demonstrate Portfolio Construction
- Demonstrate Hedging of a Vanilla Option Position
- Describe Quadratic Forms
- Discuss the Variance of Portfolio Returns as a Quadratic Form
- Define Positive Definiteness
- Demonstrate Cholesky Decomposition
- Demonstrate Eigenvalues and Eigenvectors
- Describe Principal Components

#### Probability Theory

- Explain the concept of probability
- Describe the different approaches to defining and measuring probability
- Demonstrate the rules of probability
- Define the discrete and continuous random variable
- Describe the probability distributions of a random variable
- Describe Probability density functions and histograms
- Describe the Algebra of Random variables
- Define the Expected Value and Variance of a discrete random variable
- Describe the Algebra of Continuous Random Variables
- Demonstrate Joint Probability Distributions
- Discuss covariance and correlation
- Discuss linear combinations of random variables
- Discuss the Binomial Distribution
- Demonstrate the Poisson Distribution
- Describe the Uniform Continuous Distribution
- Discuss the Normal Distribution
- Discuss the Lognormal Probability Distribution and its use in derivative pricing
- Discuss the Student’s t Distribution
- Discuss the Bivariate Normal Joint Distribution

#### Regression Analysis

- Define Regression Analysis and the different types of regression
- Demonstrate Simple Linear Regression
- Demonstrate Multiple Linear Regression
- Discuss the evaluation of the Regression Model
- Describe Confidence Intervals
- Describe Hypothesis Testing
- Demonstrate Significance Tests for the Regression Parameters
- Demonstrate Significance Test for R
_{2} - Describe Type I and Type II Errors
- Demonstrate the concept of Prediction
- Describe the OLS Assumptions and main breakdowns of them
- Describe Random Walks and Mean Reversion
- Describe Maximum Likelihood Estimation

#### Numerical Methods

- Demonstrate the Bisection method for solving Non-differential Equations
- Demonstrate the Newton-Raphson method for solving Non-differential Equations
- Describe the application of Goal Seek equation solver in Excel
- Demonstrate Unconstrained Numerical Optimisation
- Demonstrate Constrained Numerical Optimisation
- Demonstrate Binomial Lattices for valuing options
- Demonstrate Finite Difference Methods for valuing options
- Demonstrate Simulation using Excel