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<h2> Discrete Mathematics</h2> <br>
<b> Course outlines: </b> <br><br>
<b> Introduction to propositional logic:</b> Motivation, Discrete objects, Proposition, Connectives, Truth table, Compound statement, Propositional equivalence,
Tautology, Contradiction, Contingency, Laws of proposition, Dual of proposition, Argument and its validity, Predicates or Propositional function,
Quantifiers: universal and existential quantifiers. <br><br>
<b> Introduction, Sets & Functions: </b> Sets, Operations on sets, Power set, Inclusion and exclusion principle, Multi set, Operations on
multi sets, Cartesian product, Binary relation, Domain and range of relation, Complement of relation, Inverse of relation, Composition of relation, Types of
relation, Equivalence relation, Partial order relation, Partially ordered set, Well ordered set, Maximal and minimal element, Infimum and Supremum, Order
completeness axiom, Similar sets, Countable set, Uncountable set. <br> <br>
<b> Proof Techniques: </b> Direct proof, Proof by contradiction, Proof by contrapositive, Proof by cases, Proof by counter example, Proof by mathematical
induction: Various form of mathematical induction Deductions, Resolution, Mathematical proofs. <br><br>
<b> Counting & Combinatorics: </b> Counting, Sum and product rule, Principle of inclusion exclusion, Pigeon hole principal, Counting by bijection, Linear
recurrence relation-method of solutions, Generating functions, Permutations and counting. <br><br>
<b> Basic graph theory: </b> Graph, Subgraphs, Constructions of new graphs from existing graphs, Connected graph, Isomorphism, Walks, Paths, Cycle, Tree,
Euler graph, Hamiltonian graph, Planar graph, Graph homeomorphism, Kuratowski’s Theorem. <br> <br>
<b> Algebraic structures: </b> Group, Subgroups, Lagrange theorem, Rings and Fields.<br><br>
<b> Text book: </b> Kenneth H. Rosen, Discrete mathematics and its application, Tata McGraw Hill. <br><br>
<b> Reference books: </b>
1: Eric Lehman, F Thomson Leighton, Albert R Meyer, Mathematics for computer science. <br>
2: Huth and Ryan, Logic in computer science, Cambridge University Press.
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<font size=4> <b> DMS Lectures </b></font> </p>
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<td height="19" align="center" width="190"> <B><FONT> Lectures
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Link </FONT></B></td>
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<td width="320"> Lecture 0 (Motivation) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l0.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 1 (Proposition and its equivalence) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l1.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 2 (Predicates and Quantifiers) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l2.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 3 (Basics of Set Theory) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l3.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 4 (Relations and Equivalence Relation) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l4.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 5 (Partial Order Relation) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l5.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 6 (Equivalent Sets) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l6.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 7 (Countable and uncountable Sets) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l7.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 8 (Proof Techniques) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l8.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 9 (Counting Techniques) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l9.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 10 (Recurrence Relation) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l10.pdf"> PDF </a></b></font>
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<td width="320"> Lecture 11 (Generating function) </td>
<td width="100" align="center">
<font size="2"><b>
<a href="pdf\l11.pdf"> PDF </a></b></font>
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<p style="line-height: 10%">
<font size=4> <b> DMS Tutorials </b></font> </p>
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<td height="19" align="center" width="183"> <B><FONT> Tutorial Sheet
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Link </FONT></B></td>
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<td width="280"> Tutorial Sheet 1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\dms_tut_1.pdf"> PDF </a></b></font>
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<td width="280"> Tutorial Sheet 2 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\dms_tut_2.pdf"> PDF </a></b></font>
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<td width="280"> Tutorial Sheet 3 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\dms_tut_3.pdf"> PDF </a></b></font>
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<td width="280"> Tutorial Sheet 4 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\dms_tut_4.pdf"> PDF </a></b></font>
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<td width="280"> Tutorial Sheet 5 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\dms_tut_5.pdf"> PDF </a></b></font>
</table>
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