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<h1> Discrete Mathematics</h1> <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,
<br> 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, Algebra of sets,
Power set, Inclusion and exclusion principle, <br> Multi set, Operations on
multi sets, Cartesian product,
Binary relation, Domain and range of relation, Complement of relation, Inverse of relation, <br>
Composition of relation, Types of relation, Equivalence relation, Partial order relation, Partially ordered set, Well ordered set, Maximal and minimal element,
<br> Infimum and Supremum, Order completeness axiom, Functions, Types of
functions. 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 <br> 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,<br> Double counting, Linear recurrence relation-method
of solutions, Generating functions, Permutations and counting. <br><br>
<b> Basic graph theory: </b> Graph, Subgraphs, Isomorphism, Walks, Paths, Circuits, Euler graph,
Hamiltonian graph, Planar graph. <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>
<b> Reference books: </b> <br>
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. <br>
<h2> </h2>
<p align="left"><font color="black" size="4"><b> <br>
<a href="pdf\Timetable(DMS).pdf"> Lecture & Tutorial schedule </a> <br><br>
<h2> </h2> <br>
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="AutoNumber1" height="449">
<tr>
<td width="43%" height="449">
<p style="line-height: 10%">
<font size=4> <b> Tutorial discription </b></font> </p>
<div align="left">
<table border="1" cellpadding="2" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" width="503" id="AutoNumber2">
<tr>
<td height="19" align="center" width="183"> <B><FONT> Topics
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Tutorial Sheet </FONT></B></td>
</tr>
<tr>
<td width="280"> Tutorial Sheet-1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\Tutorial Sheet-1.pdf"> PDF </a></b></font>
</td>
</tr>
<tr>
<td width="280"> Tutorial Sheet-2 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\Tutorial Sheet-2.pdf"> PDF </a></b></font>
</tr>
<tr>
<td width="280"> Tutorial Sheet 3 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\Tutorial Sheet-3.pdf"> PDF </a></b></font>
</tr>
<td width="280"> Tutorial Sheet 4 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\Tutorial Sheet-4.pdf"> PDF </a></b></font>
</tr>
<td width="280"> Tutorial Sheet 5 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\Tutorial Sheet-5.pdf"> PDF </a></b></font>
</tr>
</table>
<br><br>
<h2>Tentative Assesment Schedule</h2>
<table border = "1">
<tr>
<th>Component
<th>Assesment
<th>Date
</tr>
<tr>
<td rowspan = "2">C-1
<td>Quiz-1
<td>6th April
</tr>
<tr>
<td>Review Test-1
<td>24th April
</tr>
<tr>
<td rowspan = "2">C-2
<td>Quiz-2
<td>17th May
</tr>
<tr>
<td>Review Test-2</td>
<td>31st May</td>
</tr>
<tr>
<td rowspan = "2">C-3
<td>Review test-3
<td>19th June
</tr>
</table>
<br><br>
<h2> </h2> <br>
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="AutoNumber1" height="449">
<tr>
<td width="43%" height="449">
<p style="line-height: 10%">
<font size=4> <b> Marking Schemes </b></font> </p>
<div align="left">
<table border="1" cellpadding="2" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" width="503" id="AutoNumber2">
<tr>
<td height="19" align="center" width="183"> <B><FONT> Exams
</FONT></B> </td>
<td width="80" align="center"> <B><FONT> Marking Scheme </FONT></B></td>
</tr>
<tr>
<td width="280"> Quiz-1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\C1 Quiz MS.pdf"> PDF </a></b></font>
</td>
</tr>
<tr>
<td width="280"> Review Test-1 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\C1 Review MS.pdf"> PDF </a></b></font>
</tr>
<tr>
<td width="280"> Quiz-2 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\C3(MS).pdf"> PDF </a></b></font>
</tr>
<tr>
<td width="280"> Review Test-2 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\C3(MS).pdf"> PDF </a></b></font>
</tr>
<tr>
<td width="280"> Review Test-3 </td>
<td width="280" align="center">
<font size="2"><b>
<a href="pdf\C3(MS).pdf"> PDF </a></b></font>
</tr>
</table>
<br><br>
</header>
<br><br><br><br><br>
<content>
<center><h3 class="toggler-37">DMS Marks: Jan - July, 2023</h3></center>
<ul class="panel-37">
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//******************************************************
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?>
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<tr><td><b><u>Exam </u></b></td><td><b><u>Mark</u></b></td></tr>
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<tbody>
<?php
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<h4>Log-In using your LDAP credentials</h4>
<form action="#" method="POST">
<label for="username">Username: </label><br>
<input id="username" type="text" name="username" /><br>
<label for="password">Password: </label><br>
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</ul>
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