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 Semivariance and Negative Semideviation
 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 Nondifferential Equations
 Demonstrate the NewtonRaphson method for solving Nondifferential 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
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