Pre-requisite: Knowledge and understanding of basic constructs of a programming language

### Mathematics

- Basic Number theory
- Sets
- Venn diagrams
- Set builder notations
- subsets
- Union, intersections, difference, membership
- Set equality
- Empty, Universal sets
- Types of numbers and their symbols

- Relations and Functions
- Relations: Intuitive idea - member of set A is related to member of set B
- Relations: Bigger picture - subsets of cartesian products
- Concept of domain, co-domain of a relation
- Direction in a relation
- No pre-image can have more than one image
- Concept of functions
- Concept of domain, range of a function
- Functions: Dependent and Independent variables

- Intro to combinatorics
- Principle of counting
- Selection
- Permutation
- Factorials
- Combinations

- Logarithms
- Idea of what is exactly logarithm of a number.
- Properties.
- Examples

- Complexity Analysis
- Notions of efficiency
- How to measure efficiency - express runtime as a function of input size
- Examples of measuring efficiency of some problems
- Comparison of functions
- Big-O notation

### Language Constructs - C++ - 1

- Introduction to C++
- What is C++?
- Why do we need another language?
- Basic Structure of a C++ program

- Data types
- Recap of data types in Python
- Declaring and initializing variables of different data types in C++.
- Primitives datatypes in C++
- int
- long long
- float
- double
- char
- Bool

- Overflow of values
- Arrays
- Motivation
- Arrays in C++ including implementation
- Difference between python lists and C++ array

- Control flow
- Decision Making statements
- if
- else if
- else

- and, or, not operators
- Loops
- for
- while

- Decision Making statements
- I / O
- Introduction(Motivation)
- Concept of Streams
- Input using cin
- Input using getline
- Output using cout

- Functions
- return types
- Parameters
- By value
- By reference

- Recursion
- Notion of Structs
- Basic Idea of an user defined data type.
- Motivational Problem
- Implementation in C++

### Algorithms and data structures - 1

- Searching
- Motivational Problem
- Linear Search
- Binary Search
- Algorithm
- Complexity
- Code

- Think about implementing your own lower_bound().

- Sorting
- Insertion sort
- Algorithm
- Visualization
- Code
- Complexity Analysis

- Merge sort
- Merging two small sorted arrays to get another sorted array(Algorithm).
- The idea of Divide and Conquer
- Algorithm
- Visualization
- Code
- Complexity Analysis

- Insertion sort

### Language Constructs - C++ 2

- STL - Containers(stack + queue + priority queue)
- Stack(Motivational Problem, some important functions, LIFO)
- Queues(Motivational Problem, some important functions, FIFO)
- Priority Queues(Motivational Problem, some important functions)

- STL - Containers(string + vector + pair)
- Strings(Basic idea, some important functions)
- Vector(Basic idea, some important functions)
- Pair(Basic idea, some important functions)
- Appendix: Iterators

- STL - Algorithms + Set + Map
- sort
- upper_bound
- lower_bound
- set(Basic idea, some important functions of set container)
- map(Basic idea, some important functions of map container)

- Structs - Using them as comparators
- Basic Idea of comparators
- Implementation in C++.

### Algorithms and data structures - 2

- Dynamic Programming(DP)
- Concept of Subproblem of a problem and overlapping subproblems.
- DP as Recursion+Memoization
- Linear DPs
- Multi-dimensional DP

- Graphs and Graph Algorithms
- Modelling problems as graphs
- Types of Graphs
- Undirected Graphs
- Directed Graphs

- Representation of graphs
- Adjacency Matrix
- Adjacency list

- Depth First Search(Algorithm, Code, Visualization)
- Breadth First Search(Algorithm, Code, Visualization)
- (Optional) Shortest Path Algorithms(Algorithms, Codes, Visualizations)

- Sieves
- Sieve of Eratosthenes

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