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Discrete Mathematics -Paper Pattern


Course Objectives: 

  • To use appropriate set, function and relation models to understand practical examples, and interpret the associated operations and terminologies in context. 
  • Determine number of logical possibilities of events. 
  • Learn logic and proof techniques to expand mathematical maturity. 
  • Formulate problems precisely, solve the problems, apply formal proof techniques, and explain the reasoning clearly.

Course Outcomes: 


On completion of the course, student will be able to– 

  • Solve real world problems logically using appropriate set, function, and relation models and interpret the associated operations and terminologies in context. 
  • Analyze and synthesize the real world problems using discrete mathematics. 


Course Contents
Unit I :
Set Theory and Logic -09 Hours 

Discrete Mathematics, Significance of Discrete Mathematics in Computer Engineering.
  • Sets– Naïve Set Theory (Cantorian Set Theory), Axiomatic Set Theory, Need for Sets, Representation of Sets, Set Operations, cardinality of set, principle of inclusion and exclusion.
  • Types of Sets – Countable and Uncountable Sets, Finite and Infinite Sets, Countably Infinite and Uncountably Infinite Sets. Introduction to bounded and unbounded sets and multiset. Countability of Rational Numbers Using Cantor Diagonalization Argument, power set. 
  • Propositional Logic- logic, Propositional Equivalences, Application of Propositional Logic-Translating English Sentences, Proof by Mathematical Induction and Strong Mathematical Induction.
 Unit II
 Relations and Functions -09 Hours 
  • Relations and Their Properties, n-ary Relations and Their Applications, Representing Relations , Closures of Relations, Equivalence Relations, Partial Orderings, partitions, Hasse Diagram, Lattices, Chains and Anti-Chains, Transitive Closure and Warshall‘s Algorithm, n-Ary Relations and their Applications.
  •  Functions- Surjective, Injective and Bijective functions, Inverse Functions and Compositions of Functions, The Pigeonhole Principle.

Unit III 
Counting -09 Hours 

The Basics of Counting, rule of Sum and Product, Permutations and Combinations, Binomial Coefficients and Identities, Generalized Permutations and Combinations, Algorithms for generating Permutations and Combinations. 


Unit IV 
Graph Theory -09 Hours 

Graphs and Graph Models, Graph Terminology and Special Types of Graphs, Representing Graphs and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Single source shortest path- Dijkstra's Algorithm, Planar Graphs, Graph Colouring. Case Study- Web Graph, Google map.

Unit V 
Trees -09 Hours 

Introduction, properties of trees, Binary search tree, decision tree, prefix codes and Huffman coding, cut sets, Spanning Trees and Minimum Spanning Tree, Kruskal‘s and Prim‘s algorithms, The Max flow- Min Cut Theorem (Transport network). Case Study- Game Tree, Mini-Max Tree. 

Unit VI 
Algebraic Structures and Coding Theory -09 Hours

The structure of algebra, Algebraic Systems, Semi Groups, Monoids, Groups, Homomorphism and Normal Subgroups, and congruence relations, Rings, Integral Domains and Fields, coding theory, Polynomial Rings and polynomial Codes, Case Study- Brief introduction to Galois Theory –Field Theory and Group Theory. 


 REFERENCE BOOKS

1. Kenneth H. Rosen, ―Discrete Mathematics and its Applications‖, Tata McGraw-Hill, ISBN 978-0-07-288008-3, 7th Edition.

 2. C. L. Liu, ―Elements of Discrete Mathematics‖, TMH, ISBN 10:0-07-066913-9.

3. Bernard Kolman, Robert C. Busby and Sharon Ross, ―Discrete Mathematical Structures‖, Prentice-Hall of India /Pearson, ISBN: 0132078457, 9780132078450. 

4. N. Biggs, ―Discrete Mathematics‖, 3rd Edition, Oxford University Press, ISBN 0 –19 850717 – 8.

 5. Narsingh Deo, ―Graph with application to Engineering and Computer Science‖, Prentice Hall of India, 1990, 0 – 87692 – 145 –

 6. Dr. K. D. Joshi, ―Foundations of Discrete Mathematics‖, New Age International Limited, Publishers, January 1996, ISBN: 8122408265, 9788122408263

 7. C.D. Cantrell, ―Modern Mathematical Methods for Engineers‖, Cambridge University Press, ISBN-0521670497 

8. Eric Gossett, ―Discrete Mathematical Structures with Proofs‖, Wiley India Ltd, ISBN:978-81-265-2758-8.

 9. Sriram P & Steven S, ―Computational Discrete Mathematics‖, Cambridge University Press, ISBN 13: 978-0-521-73311-3.

FREE PAID E-BOOKS ::

(CLICK THE TITLE BUTTON TO DOWNLOAD  E-BOOKS)

Kenneth H. Rosen, ―Discrete Mathematics and its Applications‖, Tata McGraw-Hill, ISBN 978-0-07-288008-3, 7th Edition.


C. L. Liu, ―Elements of Discrete Mathematics‖, TMH, ISBN 10:0-07-066913-9.

Schaum's Outlines Discrete Mathematics

Discrete Mathematics For Computer Science





 UDEMY COURSES

Udemy.com is an online learning platform. It is aimed at professional adults. Unlike academic massive open online course (MOOC) programs which are driven by traditional collegiate coursework, Udemy uses content from online content creators to sell for profit. Udemy provides tools which enable users to create a course, promote it and earn money from student tuition charges.
No Udemy courses are currently credentialed for college credit; students take courses largely as a means of improving job-related skills. Some courses generate credit toward technical certification. Udemy has made a special effort to attract corporate trainers seeking to create coursework for employees of their company.
As of 2018, there are more than 130,000 courses on the website




FREE UDEMY COURSES (2019)

1.C++ Tutorial For Complete Beginners       
2.Java Tutorials For Complete Beginners  
3.HTML & CSS For Beginners

4.APP DEVELOPMENT WITH SWIFT(Downloadable)

5. 1 HOUR HTML(Downloadable)

6. 1 HOUR JAVASCRIPT (Downloadable)

7. 3D MOTIVE MODEL AND SCULPT SYTILISED



8.ADOBE LIGHTROOM 5

9.ADVANCED SQL TUTORIAL

10.COMPLETE PHP COURSE -WEBSITE DEVELOPMENT

11.C Programming For Complete Beginners

12.The Data Science Course 2018 Complete Data Science Bootcamp – Udemy

13.Complete Forex Course Beginner to Professional

14.Stock Trading & Investing For Beginners

15.Udemy – c++ Programming Step By Step From Beginner To Advance Level 




Savitribai Phule Pune University 
First Year Engineering (2019 Course) 
107001 – Engineering Mathematics – I

   

Examination Scheme: {Credits 04}
In-Semester Exam :30 Marks 
End-Semester Exam :70 Marks 
Term Work :25 Marks 


Prerequisites:
  • Differentiation.
  • Integration.
  • Maxima and Minima.
  • Determinants and Matrices. 

Course Objectives:

  •  To make the students familiarize with concepts and techniques in Calculus, Fourier series and Matrices.
  •  The aim is to equip them with the techniques to understand advanced level mathematics and 
  • Its applications that would enhance analytical thinking power, useful in their disciplines.
Course Outcomes (COs): 

The students will be able to learn:

Course Outcomes -1:
Mean value theorems and its generalizations leading to Taylors and Maclaurin’s series useful in the analysis of engineering problems. 
Course Outcomes-2: 
The Fourier series representation and harmonic analysis for design and analysis of periodic continuous and discrete systems.
Course Outcomes-3: 
To deal withderivative of functions of several variables that are essential in various branches of Engineering. 
Course Outcomes-4: 
To apply the concept of Jacobian to find partial derivative of implicit function and functional dependence. Use of partial derivatives in estimating error and approximation and finding extreme values of the function.
Course Outcomes-5: 
The essential tool of matrices and linear algebra in a comprehensive manner for analysis of system of linear equations, finding linear and orthogonal transformations, Eigen values and Eigen vectors applicable to engineering problems.


Course Contents:

Unit I : Differential Calculus:  Rolle’s Theorem, Mean Value Theorems, Taylor's Series and Maclaurin's Series, Expansion of functions using standard expansions, Indeterminate Forms, L' Hospital's Rule, Evaluation of Limits and Applications. (08 Hrs.)

Unit II : Fourier Series  Definition, Dirichlet’s conditions, Full range Fourier series, Half range Fourier series, Harmonic analysis, Parseval’s identity and Applications to problems in Engineering. 

Unit III : Partial Differentiation  Introduction to functions of several variables, Partial Derivatives, Euler's Theorem on Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change of Independent variables  (08Hrs.)

Unit IV : Applications of Partial Differentiation  Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions of two variables, Lagrange's method of undetermined multipliers.  (08 Hrs.)

Unit V : Linear Algebra-Matrices, System of Linear Equations  Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear and Orthogonal Transformations, Application to problems in Engineering.   (08 Hrs.)

Unit VI : Linear Algebra-Eigen Values and Eigen Vectors, Diagonaliztion ,Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonaliztion of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.


RECOMMENDED TEXT BOOKS:
1. Higher Engineering Mathematics by B. V. Ramana (Tata McGraw Hill) 

REFERENCE BOOKS: 
2. Advanced Engineering Mathematics by M. D. Greenberg (Pearson Education) 
3. Advanced Engineering Mathematics by Peter V. O’Neil (Thomson Learning) 
4. Thomas’ Calculus by George B. Thomas, (Addison-Wesley, Pearson) 
5. Applied Mathematics (Vol. I & Vol. II) by P.N.Wartikar and J.N.Wartikar Vidyarthi Griha Prakashan, Pune. 
6. Linear Algebra –An Introduction, Ron Larson, David C. Falvo (Cenage Learning, Indian edition)

 BUY

Tutorial and Term Work:
 i) Tutorial for the subject shall be engaged in minimum three batches (batch size of 22 students maximum) per division. 
ii) Term work shall consist of six assignments on each unit-I to unit-VI and is based on performance and continuous internal assessment




What is an HTML File?


  •  HTML stands for Hyper Text Markup Language 
  • An HTML file is a text file containing small markup tags
  • The markup tags tell the Web browser how to display the page 
  • An HTML file must have an htm or html file extension 
  • An HTML file can be created using a simple text editor
If you are running Windows, start Notepad.
Type in the following text:
<html>
<head>
<title>Title of page</title>
</head>
<body>
This is my first homepage. <b>This text is bold</b>
</body>
</html>
Save the file as "mypage.htm".
Start your Internet browser. Select "Open" (or "Open Page") in the File menu of
your browser. A dialog box will appear. Select "Browse" (or "Choose File") and locate the HTML file you just created - "mypage.htm" - select it and click "Open".
Now you should see an address in the dialog box, for example
"C:\MyDocuments\mypage.htm". Click OK, and the browser will display the page.
Example Explained::

  • -The first tag in your HTML document is <html>. -This tag tells your browser that this is the start of an HTML document. The last tag in your document is </html>.
  • -This tag tells your browser that this is the end of the HTML document.
  • -The text between the <head> tag and the </head> tag is header information.
  • -Header information is not displayed in the browser window.
  • -The text between the <title> tags is the title of your document. The title is displayed in your browser's caption.
  • -The text between the <body> tags is the text that will be displayed in your browser.
  • -The text between the <b> and </b> tags will be displayed in a bold font.



HTML Or HTML EXTENSION

When you save an HTML file, you can use either the .htm or the .html extension.
We have used .htm in our examples. It might be a bad habit inherited from the
past when some of the commonly used software only allowed three letter
extensions.
With newer software we think it will be perfectly safe to use .html.
Note on HTML Editors:
You can easily edit HTML files using a WYSIWYG (what you see is what you get)
editor like FrontPage, Claris Home Page, or Adobe PageMill instead of writing your
markup tags in a plain text file.
But if you want to be a skillful Web developer, we strongly recommend that you
use a plain text editor to learn your primer HTML.
HTML Elements
HTML documents are text files made up of HTML elements.
HTML elements are defined using HTML tags.
HTML Tags
 HTML tags are used to mark-up HTML elements
 HTML tags are surrounded by the two characters < and >
 The surrounding characters are called angle brackets
 HTML tags normally come in pairs like <b> and </b>
 The first tag in a pair is the start tag, the second tag is the end tag
 The text between the start and end tags is the element content
 HTML tags are not case sensitive, <b> means the same as <B>

HTML Elements

Remember the HTML example from the previous page:
<html>
<head>
<title>Title of page</title>
</head>
<body>
This is my first homepage. <b>This text is bold</b>
</body>
</html>
This is an HTML element:
<b>This text is bold</b>
The HTML element starts with a start tag: <b>
The content of the HTML element is: This text is bold
The HTML element ends with an end tag: </b>
The purpose of the <b> tag is to define an HTML element that should be displayed
as bold.
This is also an HTML element:
<body>
This is my first homepage. <b>This text is bold</b>
</body>
This HTML element starts with the start tag <body>, and ends with the end tag
</body>.
The purpose of the <body> tag is to define the HTML element that contains the
body of the HTML document.
Why do We Use Lowercase Tags?
We have just said that HTML tags are not case sensitive: <B> means the same as
<b>. When you surf the Web, you will notice that most tutorials use uppercase
HTML tags in their examples. We always use lowercase tags. Why?
If you want to prepare yourself for the next generations of HTML you should start
using lowercase tags. The World Wide Web Consortium (W3C) recommends
lowercase tags in their HTML 4 recommendation, and XHTML (the next generation
HTML) demands lowercase tags.
Tag Attributes
Tags can have attributes. Attributes can provide additional information about the
HTML elements on your page.
This tag defines the body element of your HTML page: <body>. With an added bgcolor attribute, you can tell the browser that the background color of your page
should be red, like this: <body bgcolor="red">.
This tag defines an HTML table: <table>. With an added border attribute, you can
tell the browser that the table should have no borders: <table border="0">
Attributes always come in name/value pairs like this: name="value".
Attributes are always added to the start tag of an HTML element.
Quotes Style ,"red" or 'red' ?
Attribute values should always be enclosed in quotes. Double style quotes are the
most common, but single style quotes are also allowed.
In some rare situations, like when the attribute value itself contains quotes, it is
necessary to use single quotes:
name='John "ShotGun" Nelson'

HTML TAGS

Basic HTML Tags

The most important tags in HTML are tags that define headings,
paragraphs and line breaks.
Headings
Headings are defined with the <h1> to <h6> tags. <h1> defines the largest
heading. <h6> defines the smallest heading.
<h1>This is a heading</h1>
<h2>This is a heading</h2>
<h3>This is a heading</h3>
<h4>This is a heading</h4>
<h5>This is a heading</h5>
<h6>This is a heading</h6>
HTML automatically adds an extra blank line before and after a heading.
Paragraphs
Paragraphs are defined with the <p> tag.
<p>This is a paragraph</p>
<p>This is another paragraph</p>
HTML automatically adds an extra blank line before and after a paragraph.
Line Breaks
The <br> tag is used when you want to end a line, but don't want to start a new
paragraph. The <br> tag forces a line break wherever you place it.
<p>This <br> is a para<br>graph with line breaks</p>
The <br> tag is an empty tag. It has no closing tag.
Comments in HTML
The comment tag is used to insert a comment in the HTML source code. A
comment will be ignored by the browser. You can use comments to explain your
code, which can help you when you edit the source code at a later date.
<!-- This is a comment -->
Note that you need an exclamation point after the opening bracket, but not before
the closing bracket.
Basic HTML Tags
Tag Description
<html> Defines an HTML document
<body> Defines the document's body
<h1> to <h6> Defines header 1 to header 6
<p> Defines a paragraph
<br> Inserts a single line break
<hr> Defines a horizontal rule
<!--> Defines a comment

HTML Text Formatting

HTML defines a lot of elements for formatting output, like bold or italic
text.
How to View HTML Source
Have you ever seen a Web page and wondered "How do they do that?"
To find out, simply click on the VIEW option in your browsers toolbar and select
SOURCE or PAGE SOURCE. This will open a window that shows you the actual
HTML of the page.
Text Formatting Tags
Tag Description
<b> Defines bold text
<big> Defines big text
<em> Defines emphasized text
<i> Defines italic text
<small> Defines small text
<strong> Defines strong text
<sub> Defines subscripted text
<sup> Defines superscripted text
<ins> Defines inserted text
<del> Defines deleted text
<s> Deprecated. Use <del> instead
<strike> Deprecated. Use <del> instead
<u> Deprecated. Use styles instead



HTML Character Entities

Some characters like the < character, have a special meaning in HTML,
and therefore cannot be used in the text.
To display a less than sign (<) in HTML, we have to use a character entity.
Character Entities
Some characters have a special meaning in HTML, like the less than sign (<) that
defines the start of an HTML tag. If we want the browser to actually display these
characters we must insert character entities in the HTML source.
A character entity has three parts: an ampersand (&), an entity name or a # and an entity number, and finally a semicolon (;).
To display a less than sign in an HTML document we must write: &lt; or &#60;
The advantage of using a name instead of a number is that a name is easier to remember. The disadvantage is that not all browsers support the newest entity names, while the support for entity numbers is very good in almost all browsers.
Note that the entities are case sensitive.
Non-breaking Space
The most common character entity in HTML is the non-breaking space.
Normally HTML will truncate spaces in your text. If you write 10 spaces in your
text HTML will remove 9 of them. To add spaces to your text, use the &nbsp;
character entity.
The Most Common Character Entities:
Result Description Entity Name Entity Number
non-breaking space &nbsp; &#160;
< less than &lt; &#60;
> greater than &gt; &#62;
& ampersand &amp; &#38;
" quotation mark &quot; &#34;
' apostrophe &apos; &#39;
Some Other Commonly Used Character Entities:
Result Description Entity Name Entity Number
¢ cent &cent; &#162;
£ pound &pound; &#163;
¥ yen &yen; &#165;
§ section &sect; &#167;
© copyright &copy; &#169;
® registered trademark &reg; &#174;
× multiplication &times; &#215;
÷ division &divide; &#247;
Frame Tags
Tag Description
<frameset> Defines a set of frames
<frame> Defines a sub window (a frame)
<noframes> Defines a noframe section for browsers that do not handle frames
<iframe> Defines an inline sub window (frame)

HTML Tables

With HTML you can create tables.
Tables
Tables are defined with the <table> tag. A table is divided into rows (with the
<tr> tag), and each row is divided into data cells (with the <td> tag). The letters
td stands for "table data," which is the content of a data cell. A data cell can
contain text, images, lists, paragraphs, forms, horizontal rules, tables, etc.
<table border="1">
<tr>
<td>row 1, cell 1</td>
<td>row 1, cell 2</td>
</tr>
<tr>
<td>row 2, cell 1</td>
<td>row 2, cell 2</td>
</tr>
</table>
How it looks in a browser:
row 1, cell 1 row 1, cell 2
row 2, cell 1 row 2, cell 2
Tables and the Border Attribute
If you do not specify a border attribute the table will be displayed without any
borders. Sometimes this can be useful, but most of the time, you want the borders
to show.
To display a table with borders, you will have to use the border attribute:
<table border="1">
<tr>
<td>Row 1, cell 1</td>
<td>Row 1, cell 2</td>
</tr>
</table>
Headings in a Table
Headings in a table are defined with the <th> tag.
<table border="1">
<tr>
<th>Heading</th>
<th>Another Heading</th>
</tr>
<tr>
<td>row 1, cell 1</td>
<td>row 1, cell 2</td>
</tr>
<tr>
<td>row 2, cell 1</td>
<td>row 2, cell 2</td>
</tr>
</table>
How it looks in a browser:
Heading Another Heading
row 1, cell 1 row 1, cell 2
row 2, cell 1 row 2, cell 2
Empty Cells in a Table
Table cells with no content are not displayed very well in most browsers.
<table border="1">
<tr>
<td>row 1, cell 1</td>
<td>row 1, cell 2</td>
</tr>
<tr>
<td>row 2, cell 1</td>
<td></td>
</tr>
</table>
How it looks in a browser:
row 1, cell 1 row 1, cell 2
row 2, cell 1
Note that the borders around the empty table cell are missing.
To avoid this, add a non-breaking space (&nbsp;) to empty data cells, to make the
borders visible:
<table border="1">
<tr>
<td>row 1, cell 1</td>
<td>row 1, cell 2</td>
</tr>
<tr>
<td>row 2, cell 1</td>
<td>&nbsp;</td>
</tr>
</table>
How it looks in a browser:
row 1, cell 1 row 1, cell 2
row 2, cell 1
Table Tags
Tag Description
<table> Defines a table
<th> Defines a table header
<tr> Defines a table row
<td> Defines a table cell
<caption> Defines a table caption
<colgroup> Defines groups of table columns
<col> Defines the attribute values for one or more columns in a table
<thead> Defines a table head
<tbody> Defines a table body
<tfoot> Defines a table footer

HTML Images

With HTML you can display images in a document.
The Image Tag and the Src Attribute
In HTML, images are defined with the <img> tag.
The <img> tag is empty, which means that it contains attributes only and it has
no closing tag.
To display an image on a page, you need to use the src attribute. Src stands for
"source". The value of the src attribute is the URL of the image you want to display
on your page.
The syntax of defining an image:
<img src="url">
The URL points to the location where the image is stored. An image named
"boat.gif" located in the directory "images" on "www.schools.com" has the URL:
http://www.schools.com/images/boat.gif.
The browser puts the image where the image tag occurs in the document. If you
put an image tag between two paragraphs, the browser shows the first paragraph,
then the image, and then the second paragraph.
The Alt Attribute
The alt attribute is used to define an "alternate text" for an image. The value of
the alt attribute is an author-defined text:
<img src="boat.gif" alt="Big Boat">
The "alt" attribute tells the reader what he or she is missing on a page if the
browser can't load images. The browser will then display the alternate text instead
of the image. It is a good practice to include the "alt" attribute for each image on a
page, to improve the display and usefulness of your document for people who
have text-only browsers.
Image Tags
Tag Description
<img> Defines an image
<map> Defines an image map
<area> Defines an area inside an image map


HTML Backgrounds

A good background can make a Web site look really great.
Backgrounds
The <body> tag has two attributes where you can specify backgrounds. The
background can be a color or an image.
Bgcolor
The bgcolor attribute sets the background to a color. The value of this attribute
can be a hexadecimal number, an RGB value, or a color name.
<body bgcolor="#000000">
<body bgcolor="rgb(0,0,0)">
<body bgcolor="black">
The lines above all set the background color to black.
Background
The background attribute sets the background to an image. The value of this
attribute is the URL of the image you want to use. If the image is smaller than the
browser window, the image will repeat itself until it fills the entire browser window.
<body background="clouds.gif">
<body background="http://www.schools.com/clouds.gif">
The URL can be relative (as in the first line above) or absolute (as in the second
line above).

MASSACHUSETTS INSTITUTE OF TECHNOLOGY(MIT)


MIT - Massachusetts Institute of Technology



Founded in 1861 in response to the increasing industralization of the united states,MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. It has since played a key role in the development of many aspects of modern science,engineering,mathematics,and technology and is widely known for its innovation and academic strength,making it one of the most prestigious institutions of higher learning in the world.

Massachusetts institute of technology offers one of the best engineering degrees for students who want undergraduate research experience. MIT is preferred by engineering aspirants is that the institute presents many research opportunities through its engineering programmes that are divided among various departments like Nuclear Science, Civil Engineering, Biological Engineering and Computer Science, among others.

Institution Type       : Private
Website 
                  : http://web.mit.edu/student/
Admission Website
  : web.mit.edu/admissions/


HOW TO APPLY:

  • To apply in the Massachusetts institute of technology ( MIT)  you are required to submit your Academics scores along with GRE scores.

  • Some departments also require GRE subject test scores.

  • Besides GRE, applicants will have to show proof of their English proficiency through TOEFL scores.
  • You need to score at least 100 Out of 120 points in TOEFL IBT(Internet Based Test) to be selected for an Massachusetts institute of technology (MIT) engineering programme. In TOEFL PBT(Paper Based Test) your scores should be at least 600.
  • SAT (Scholastic Assessment Test) Score is required by the institute at the undergraduate level and in addition to SAT scores, MIT also asks for subject test scores of Science (Physics,Chemistry or Biology) and Maths.
  • Applications, generally, open in August and close around the first week of January the next year.

FEES:

Approximate total fees for the Under Graduate programme at MIT is $51,520 with room and board and other fees,The total price tag reaches $70,240 annually


RANKINGS: 


QS World University Rankings by TopUniversities

RANK 1 -2019

RANK 1 -2018

RANK 1 -2017


QS World University Rankings is one of the top international rankings measuring the popularity and performance of universities all over the world. They measure university reputation based on the impressions of higher education experts, companies who hire graduates, and teaching quality. QS also considers the ratio of international teachers and students present at universities, as well as the times research papers were mentioned by researchers. After calculating and comparing these criteria, QS ranks the universities accordingly




World University Rankings by Times Higher Education

RANK 1 - 2019

RANK 5 - 2018

RANK 5 - 2017



World University Rankings is a vital resource that provides the definitive list of the world's best universities. They look at how often they're producing new ideas, what their reputation is around the world, and how much they're contributing to science and academic fields. After calculating and comparing these criteria, THE ranks the universities accordingly.



Academic Ranking of World Universities by Shanghai Jiao Tong University

RANK 1 - 2018
RANK 4 - 2017
RANK 5 - 2016

RWU World University rankings is the first world university ranking. It ranks the world's top 1000 colleges and universities based on objective indicator. They look at the number of award-winning (Fields Medals and Nobel Prize) scientists who are located there, how much of their research is cited and referenced around the world, and how much they've contributed to different academic fields. After calculating and comparing these criteria, ARWU ranks the universities accordingly


Contact Info:


Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139, USA

617-253-1000 TDD/TTY, 
use TRS (711)

Admissions :
For questions about applying to MIT, visit the Admissions Office(opens in new window) or email admissions@mit.edu





PUNE UNIVERSITY 

ENGINEERING MECHANICS

First Year Engineering Credit System Syllabus 2015 Course


Structure for SEM-I


Structure for SEM-II







QUESTION PAPERS 

NOV-DEC 2018 to NOV-DEC 2016


ENGINEERING MECHANICS

  • NOV-DEC 2018


  • MAY-JUNE 2018

     

  • NOV-DEC 2017



  • MAY-JUNE 2017

  • NOV-DEC 2016

COURSE DETAILS :Course Chapters:Pune University
1.     Co-planar Forces
2.    Centroid and Centre of Gravity
3.    Rectilinear Motion
4.    Dependent Motion
5.    Relative Motion
6.    D' Alembert's Principle
7.    Curvilinear Motion8.    Projectile Motion9.    Work-Energy Principle
10.  Impulse - Momentum Theorem and Impact
11.  Equilibrium
12.  Beams and Compound Beams
13.  Space Forces
14.  Analysis of Trusses
15.  Analysis of Cables
16.  Analysis of Frames
17.  Friction
Course Syllabus:Statics includes: 
Coplanar Forces:Principle of statics, forces system, resolution and composition of forces. Resultant of concurrent forces. Moment of a force, Varignon's theorem, resultant of parallel force system. Couple, equivalent force system. Resultant of general force system. Distributed forces. Centroid of plane lamina and wire.Equilibrium Free body diagram, equilibrium of concurrent, parallel and general forces in a plane. Equilibrium of three forces in a plane. Types of beams- simple and compound beams, type of supports and reaction. Resultant of concurrent and parallel forces in space. Equilibrium of concurrent and parallel forces in space.Truss and Friction Two force members- analysis of plane trusses by method of joint and method of section, cables subjected to point loads. Multi force member- plane frames.Friction-law's of friction, application of friction on inclined plane. Wedges and ladders friction, application to flat belt.Dynamics, on the other hand, deals with bodies in motion and the resulting effects of application of forces with an emphasis on real world engineering applications.

Statics involves the visualizations and analysis of static equilibrium problems with an emphasis on real world engineering applications and problem solving.Dynamics, on the other hand, deals with bodies in motion and the resulting effects of application of forces with an emphasis on real world engineering applications.

Dynamics includes: Kinematics Basic concepts, equation of motion for constant acceleration and motion under gravity. Variable acceleration and motion curves. Relative motion and dependent motion.Equation of motion in Cartesian co-ordinate. Path and polar coordinates. Motion of projectiles. Kinetics Newton's Second Law of motion and its application. Newton's Second Law of motion in Cartesian and path co-ordinates of curvilinear motion of particles.Work Energy and Impulse Work, power, energy, conservative and non-conservative forces. Conservation of energy and work energy principle for motion of particle. Impulse, momentum, direct central impact and coefficient of restitution. Conservation of momentum and impulse momentum principle of particles.





PUNE UNIVERSITY RULES AND REGULATIONS 


  • In a bid to fine tune our technical education system to the global standards & practices, the Credit-Grade based performance and assessment system will be implemented with effect from June 2015 onwards for all the Under Graduate Programmes (UG) under the Faculty of Engineering, University of Pune, starting with First Year. 
  • With the advent of technology and ever-changing expectations from the Industry and Society, it has become imperative to relook at the structure and subject contents of various UG courses to make it contemporary and relevant.
  • As per the decision by the authorities of University of Pune the faculty of Engineering has prepared the credit system and structure. 
  • The revised course is of 190 credits and 1 credit is equivalent to 15 hours. Assessments in credit system consist of A) In-semester continuous assessment and B) End-semester assessment for the Theory head and Term Work/ Practical / Oral / Presentation at the end of the semester for Practical, Oral, Seminar and Project Head. 
  • The faculty of Engineering has shouldered the idea of incorporating latest advances in Science and technology and equip the subject/syllabus contents with latest and relevant topics and know-hows. 
  • Accordingly the new structure and syllabus are being introduced, to be implemented from the academic year 2015-16 from First Year and it will continue for subsequent years. 
  • The rules governing the programmes shall be as given below with suffix R, followed by the rule number. 
  • All UG programmes, under Faculty of Engineering shall be offered with credit system. 
  • All the B.E. programmes running under the Faculty of Engineering will be of four years duration. 
  • The total no. of credits required for the completion of the programme is 190 credits.
  • One credit is equivalent to 15 hours. 
  • A student is required to earn 190 credits in in a minimum period of eight semesters. 







RESULT: Based on the performance of the student in the semester examinations, the University of Pune will declare the results and issue the Semester Grade sheets. 

Success Mantra: Change the Opportunity for Success, Things Change Itself

Many times things that are wrong for others, by getting masters in them, people go on climbing up the steps of success. When we talk of changing the point of view, it means that how is our way of looking at any issue. Suppose opium or ganja is consumed, it consumes addiction. But it is also used as a pen killer. Similarly, there is hacking in the digital world.

It falls under the category of crime, but if it is ethical, then there may be enough work for the government and the society. Something similar has been said in our story of today. Increasing dependence on digital devices like mobile has also increased the risk of cyber crime.

Recently 94 crore rupees were stolen from Pune's 'Cosmos Bank' in a cyber attack. The business of fighting these crimes is not easy, because the techniques in the cyber world change rapidly. But Saket Modi achieved success in it.


How inspired for this

 Saket is the co-founder and CEO of cyber security firm 'Lucidus'. They do not only work to secure the data (information) of their clients and companies, but also provide training, services and products. They give their services to apps such as Whatsapp, Google Pay He has been honored by several institutions including Government of India for his contributions to Cyber ​​Security.




Saket Modi grew up in Kolkata. In his childhood, as a child, amateur had learned many tricks of hacking. Later he thought that he could use his capacity for good motive. His ability to think fast was also his skill. Saket explains, 'I take hacking as my lifestyle. Hacking means seeing things that others do not notice. You do something that others do not expect to do. 'He studied engineering from Jaipur. In the Ethical Hacking and Cyber ​​Forensics, he started to form his career through seminars and workshops. While studying in college, many IIMs started training ethical hacking in IITs. When he was in the last year of his engineering studies, he started with his two other friends, Vidyak Bakshi and Rahul Tyagi, and started the startup 'Lucidus'.


All three together put their deposits in the startup. This startup, which started in 2012, got support from IIT Bombay's 'startup incubator'. In 2013, he opened his startup office in New Delhi. So far, his startup had become the world's most popular name for cyber security. The Indian government gave them an opportunity to work together in many of their plans. The Government of India gave them the award of Best IT Startup. Today Saket is active in 16 countries through its services.


HOW TO SCORE HIGH IN YOUR EXAMINATIONS

FOLLOW THESE TOP 10 STEPS TO ACHIEVE MORE SUCCESS AND SCORE HIGH IN YOUR COMING EXAMINATION


1.BELEVE IN YOURSELF

THIS IS THE FOREMOST BARRIER TO BE CROSSED FOR SCORING MARKS IN EXAMS.ONE NEEDS TO BELIEVE IN HIS/HER ABILITY TO LEARN,MEMORISE AND REPRODUCE WHAT HAS BEEN LEARNT.EXAMS ARE NOTHING BUT THE TEST OF OUR FAITH,CONFIDENCE AND KNOWLEDGE.

2. FOLLOW A TIMETABLE

A WELL SET TIME TABLE ALOTTING SPECIFIC DURATION FOR STUDYING,SLEEPING,PLAYING,SURFING THE NET AND EATING CAN HELP EVERY STUDENT A LOT.EVERY ABOVE QUOTED THING HAS TO BE DONE EVERYDAY .A PROPER SCHEDULE CAN HELP A STUDENT BEAT EXAMINATION STRESS.

3.  SET EVERY DAY GOALS

PREPARATIONS SHOULD BE DONE EVERYDAY TO EXCEL ON THE DAY OF EXAMS WITHOUT DEPENDING UPON ANY MIRACLE CAPSULE TO BAIL YOU AT THE LAST MOMENT. BY SETTING EVERYDAY TARGETS AND GOALS,ONE CAN ACHIEVE INCREDIBLE RESULTS IN TERMS OF EFFICIENCY AND PERFORMANCE.

4. STAY HEALTHY

 HEALTH IS WEALTH.THIS IS ADAGE NEVER FAILS.ONLY A SOUND BODY AND SOUND MIND CAN WORK EFFICIENTLY TOWARDS ACHIEVING ANY OBJECTIVE THUS A HEALTHY BODY IS A MANDATE FOR RIGOROUS MENTAL EXERCISE THAT COMES UP DURING EXAMINATIONS.

5.PRACTICE DAILY

WE EAT DAILY ,WE SLEEP DAILY SO WHY NOT STUDY DAILY REGULAR PRACTICE  IN EVERY SUBJECT WILL KEEP STUDENTS CLOSE TO A SUBJECT.IF ONE AVOIDS ANY SUBJECT FOR MORE THAN THREE DAY IN A GO
HE /SHE IS BOUND TO LOSE INTEREST IN IT.

6.  PLAY GAMES

 PLAYING GAMES ,BOTH INDOORS AND OUTDOORS,HELP IN INCULCATING A PRACTICAL APPROACH TOWARDS DEALING WITH A PROBLEM ALONG WITH BEATING EXAMINATION STRESS.

7.PRESENTATION

TILL NOW WE HAVE DISCUSSED THE PRE -EXAM TIPS .THIS IS A CRUCIAL TIP WHILE WRITING THE EXAMINATIONS.A SYSTEMATIC AND NEAT DISPLAY OF ANSWERS CAN BOOST YOUR CHANCES OF SCORING HIGH.

8.TIME MANAGEMENT

YOU NEED TO MANAGE TIME NOT ONLY DURING EXAM PREPARATIONS,BUT ALSO AT THE TIME OF SOLVING THE QUESTION PAPER. CARRYING A WRIST WATCH DURING EXAMS IS AN EXCELLENT WAY TO MANAGE TIME WELL.YOU SHOULD ALSO TRY AND SAVE SOME TIME AT THE END OF THE PAPER TO RECHECK THE ANSWERS.

9. SLEEP WELL

  A SOUND SLEEP AT NIGHT BEFORE THE EXAMS HELP US RELAX AND REJUVENATES OUR MIND.THE TIRES BRAIN NEED ENOUGH REST AND WE NEED TO UNDERSTAND THIS.IT IS ONLY THEN THAT WE WILL BE ABLE TO MAKE THE MOST OF IT DURING EXAMINATIONS.

10. RELAX YOURSELF

THIS IS THE LAST BUT NOT HE LEAST . RELAXING IS LIKE MEDITATING .WHEN WE ARE RELAXED WE ARE THE MOST EFFICIENT IN REPRODUCING WHAT WE HAVE LEARNT.



MEMORY TIPS

To remember anything, the brain decides that thing on the basis of value and justification. The priority of the mind also works in this sequence. The first staircase to remember is to know the meaning, so remembering any thing can mean its meaning. If the meaning is not understood then there is no point in crying. Therefore, the first thing or lesson to remember, first understand its meaning, then consider its significance and value. Know then what is the justification of that matter in your life.

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