Lecture Notes
Calculus
Calculus is the mathematical study of change, divided into two main branches: differential calculus (which involves rates of change and slopes of curves), and integral calculus (generally dealing with accumulation of quantities and areas under curves). Downloadable notes on
- Limits
- Differential Calculus
- Integral Calculus
- Differential Equations
- Series
Linear algebra
Linear algebra is central to both Pure and Applied Mathematics. It is that branch of Mathematics which deals with vector spaces (often finite or countably infinite dimensional), as well as linear mappings between such spaces, initiated by a system of linear equations in several unknowns. Downloadable notes on
- Linear Equations and Matrices
- Determinants
- Vectors in R2 and R3
Numerical Methods
Numerical methods make use of algorithms that use numerical approximation for the problems of mathematical analysis. Since exact answers are often impossible to obtain in practice, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors. Downloadable notes on
- Root-finding Methods
- Iterative Methods
- Interpolating Polynomials
- Matrix Methods
- Numerical Differentiation
- Numerical Integration
- Errors
Discrete Mathematics
Discrete Mathematics is the branch of Mathematics dealing with objects that can assume only distinct and separated values. The study of topics in Discrete Mathematics usually includes the study of algorithms, their implementations, and efficiencies. Discrete mathematics is the mathematical language of computer science, and as such, its importance has increased dramatically in recent decades. Downloadable notes on
- Logic and Sets
- Proof Techniques
- Permutations and Combinations
- Recurrence Relations
- Directed Graphs
Statistics
Statistics is the study of collection, organisation, presentation, analysis and interpretation of data, with some of the ultimate aims being decision-making and forecasting, among others. Owing to its empirical roots and its focus on applications, Statistics is usually considered as a distinct mathematical science rather than a branch of Mathematics. Nevertheless, much of Statistics is non-mathematical: it ensures that data collection is undertaken in a way that produces valid conclusions. Downloadable notes on
- Data-handling
- Statistical Inference
- Probability and Distributions
- Reliability and Validity
- Multivariate Data
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