A typical B.Tech syllabus for Design and Analysis of Algorithms (DAA) covers topics like algorithm design techniques, time and space complexity analysis, and fundamental algorithms and data structures. It also includes mathematical foundations like discrete mathematics and graph theory. 

1. Introduction to Algorithms and Data Structures:

• What are algorithms and why analyze them?
• Importance of data structures: Arrays, linked lists, stacks, queues, trees, graphs.
• Algorithm design techniques:
• Divide and conquer: Merge sort, quicksort.
• Greedy algorithms: Minimum spanning tree (Kruskal, Prim), shortest path (Dijkstra).
• Dynamic programming: Fibonacci sequence, knapsack problem.
• Backtracking: N-Queens problem, graph coloring.
• Asymptotic notations: Big O, Omega, Theta notations.
• Recurrence relations: Solving recurrence relations using various methods (substitution, recursion tree, master theorem). 

2. Complexity Analysis:

• Time complexity analysis: Worst-case, best-case, average-case analysis.
• Space complexity analysis: Analyzing memory usage.
• Amortized analysis: Analyzing the average cost of a sequence of operations. 

3. Fundamental Algorithms and Data Structures:

• Searching algorithms: Linear search, binary search. 
• Sorting algorithms: Bubble sort, insertion sort, selection sort, merge sort, quicksort, heap sort. 
• Graph algorithms: Breadth-first search (BFS), depth-first search (DFS), shortest path algorithms (Dijkstra, Bellman-Ford), minimum spanning tree algorithms (Kruskal, Prim). 
• Tree algorithms: Tree traversals, binary search trees, balanced trees (AVL, red-black). 

4. Advanced Topics (May be covered depending on the specific syllabus):

• Hashing: Hash tables, hash functions, collision resolution techniques.
• String matching algorithms: Naive algorithm, Knuth-Morris-Pratt (KMP) algorithm.
• NP-completeness: Understanding NP-hard and NP-complete problems.
• Approximation algorithms: Techniques for solving optimization problems that are difficult to solve exactly.
• Probabilistic algorithms: Algorithms that use randomness to achieve better performance. 

5. Mathematical Foundations:

• Set theory: Basic concepts and operations on sets.
• Combinatorics: Counting techniques, permutations, combinations.
• Graph theory: Graph representations, graph traversals, shortest path problems.