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<h1 id="unit-i-mathematical-logic-sets-relations-and-functions">UNIT I: Mathematical Logic, Sets, Relations, and Functions</h1>
<h2 id="mathematical-logic">Mathematical Logic:</h2>
<ul>
<li>Notations, Algebra of Propositions &amp; Propositional functions</li>
<li>Logical connectives, Truth values &amp; Truth tables</li>
<li>Tautologies &amp; Contradictions, Normal Forms</li>
<li>Predicate Calculus, Quantifiers</li>
</ul>
<h2 id="set-theory">Set Theory:</h2>
<ul>
<li>Sets, Subsets, Power sets, Complement, Union and Intersection</li>
<li>De Morgan's Law, Cardinality</li>
</ul>
<h2 id="relations">Relations:</h2>
<ul>
<li>Cartesian Products, relational Matrices, properties of relations, equivalence relations</li>
</ul>
<h2 id="functions">Functions:</h2>
<ul>
<li>Injection, Surjection, Bijection, Composition of Functions, Permutations, Cardinality</li>
<li>Characteristic functions, Recursive definitions, Finite induction</li>
</ul>
<h1 id="unit-ii-lattices--boolean-algebra">UNIT II: Lattices &amp; Boolean Algebra</h1>
<h2 id="lattices">Lattices:</h2>
<ul>
<li>Lattices as Algebraic Systems, Sublattices</li>
<li>Some special lattices: Complement, Distributive, Modular</li>
</ul>
<h2 id="boolean-algebra">Boolean Algebra:</h2>
<ul>
<li>Axiomatic definitions of Boolean algebra as algebraic structures with two operations</li>
<li>Switching Circuits</li>
</ul>
<h1 id="unit-iii-groups-fields--rings">UNIT III: Groups, Fields, &amp; Rings</h1>
<h2 id="groups">Groups:</h2>
<ul>
<li>Definition of groups, axioms, permutation groups</li>
<li>Subgroups, co-sets, normal subgroups, free subgroups</li>
<li>Grammars, language</li>
</ul>
<h2 id="fields--rings">Fields &amp; Rings:</h2>
<ul>
<li>Definition and structure of fields and rings</li>
<li>Minimal Polynomials, Irreducible Polynomials</li>
<li>Polynomial roots &amp; its Applications</li>
</ul>
<h1 id="unit-iv-graphs">UNIT IV: Graphs</h1>
<h2 id="graphs">Graphs:</h2>
<ul>
<li>Simple Graph, Multigraph &amp; Pseudograph</li>
<li>Degree of a Vertex, Types of Graphs, Subgraphs, Isomorphic Graphs</li>
<li>Operations on Graphs, Paths, Cycles, and Connectivity</li>
<li>Euler and Hamilton Graphs, Shortest Path Problems (BFS, Dijkstra's Algorithm)</li>
<li>Representation of Graphs, Planar Graphs, Applications of Graph Theory</li>
</ul>
<h1 id="unit-v-trees">UNIT V: Trees</h1>
<h2 id="trees">Trees:</h2>
<ul>
<li>Definition and properties of trees, pendant vertices in a tree, center of a tree</li>
<li>Spanning tree, Binary tree, Tree traversal</li>
<li>Applications of trees in computer science</li>
</ul>

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