Discrete Mathematics Topics

 

- Introduction

*Mathematical Reasoning

*Combinatorial Analysis

*Discrete Structures

*Algorithmic Thinking

*Applications and Modeling

- Logic and Proofs

- Basic Structures

*Sets

*Functions

*Sequences

*Sums

*Matrics

- Number Theory

- Induction and Recursion

- Counting

- Discrete Probability

- Relations

- Graphs

- Trees

- Modeling Computation

MTA Exam 98-382: Introduction to Programming Using JavaScript

Program with JavaScript Operators, Methods, and Keywords

Program with Variables, Data Types, and Functions

Implement and Analyze Decisions and Loops

Interact with the Document Object Model

Interact with HTML Forms

Program with JavaScript Operators, Methods, and Keywords

Complete or debug code that uses assignment and arithmetic operators

Assignment; increment; decrement; addition; subtraction; division; multiplication; modulus; compound assignment operators

Apply JavaScript best practices  

Comments; indentations; naming conventions; noscript; constants; reserved keywords; debugger keyword; setting breakpoints; console.log

Evaluate the use of inline and external scripts

When to use, how to use, and what happens when both are used

Implement exception handling

try; catch; finally

Complete and debug code that interacts with the Browser Object Model (BOM)

Manage state; display dialogs; determine screen size

Program with Variables, Data Types, and Functions

Declare and use variables of primitive data types 

Number; Boolean; String; Null; Undefined; typeof operator; type checking functions; use strict; converting between data types; formatting numbers; string operations; single quote vs double quote (nesting); initialization

Declare and use arrays

Single-dimensional arrays; multi-dimensional arrays; iteration; initialization; define an array; sort and search an array; use push, pop, shift, and unshift methods; use the length property; access an array element;

Complete and debug code that uses objects

Properties; methods; instantiation; Date object; retrieve date and time parts; localize date format (MM/DD vs DD/MM); add and subtract dates

Complete and debug code that uses built-in Math functions

Random; round; abs; floor; ceiling; min; max; pow; sqrt

Complete and debug a function that accepts parameters and returns a value

Reusable code; local versus global scope, redefine variables, pass parameters, value versus reference, return values

Implement and Analyze Decisions and Loops

Evaluate expressions that use logical and comparison operators

==; !=; <, >; <=; >=; !; &&; ||

Complete and debug decision statements

if; else if; switch; nested if

Complete and debug loops

for; while; do; break; continue

Interact with the Document Object Model

Identify and construct the Document Object Model (DOM) tree

window; document; body; other HTML elements

Identify and handle HTML events

onchange; onmouseover; onload; onclick; onmouseout; onkeydown

Complete and debug code that  outputs to an HTML document

innerHTML; document.write

Complete and debug code that locates, modifies, and adds HTML elements and attributes

getElementByld; getElementsByTagName; getElementsByClassName; setAttribute; createElement

Interact with HTML Forms

Complete and debug code that retrieves input from forms and sets form field values

Retrieve form values; identify the DOM path; get values from different types of elements; prepopulate values; mask values

Complete and debug code that performs input validation

Case; string comparisons; Not-A-Number (NaN)

Describe the form submission process

onsubmit; post versus get; potential targets for submission

MTA Exam 98-383: Introduction to Programming Using HTML and CSS

Understand HTML Fundamentals

Understand CSS Fundamentals

Structure Documents Using HTML

Present Multimedia Using HTML

Style Web Pages Using CSS

Understand HTML Fundamentals

Construct markup that uses metadata elements

Script; noscript; style; link; meta tags, including encoding, keywords, viewport, and translate

Construct well-formed markup that conforms to industry best practices  

DOCTYPE declaration; HTML; head; body; proper syntax, including closing tags and commonly used symbols; comments

Understand CSS Fundamentals

Analyze the impact of using inline styles, internal style sheets, and external style sheets

When to use inline styles; when to use internal style sheets; when to use external style sheets; precedence when using a combination of inline styles and style sheets

Construct and analyze rule sets

Valid syntax for the CSS rule set; selectors, including class, id, elements and pseudo-class

Construct well-formed style sheets that conform to industry best practices

Reusing rules and rule sets; commenting; testing on multiple browsers; web safe fonts

Structure Documents Using HTML

Construct and analyze markup to structure content and organize data

Table tags; h1-h6; p; br; hr; div; span; ul; ol; li

Construct and analyze markup that uses HTML5 semantic elements

Semantic tags; header; nav; section; article; aside; footer; details; summary; figure; caption

Construct and analyze markup that implements navigation

Image links; a; target; bookmark; relative versus absolute links; navigating simple folder hierarchies

Construct and analyze markup that uses form elements

Form attributes; action; method; submission methods; accessibility; input types and restrictions; select; textarea; button; output; option; datalist; fieldset

Present Multimedia Using HTML

Construct and analyze markup that displays images

img and picture elements and their attributes

Describe the appropriate use of the img, svg, and canvas elements

Construct and analyze markup that plays video and audio

Video; audio; track; source; simple iframe implementations

Style Web Pages Using CSS

Construct and analyze styles that position content

Positioning, including float, relative, absolute, max-width, overflow, height, width, and align; inline versus block; visibility; box model, including margins and padding

Construct and analyze styles that format text

Font-family; color; font-style; font-size; font-weight; link colors; text formatting, including text alignment, text decoration, and indentation

Construct and analyze styles that format backgrounds and borders

Border-color; border-style; border-width; backgrounds; divs; colors

Analyze styles that implement a simple responsive layout

Units of measure; responsive effects with CSS, including viewport and media query; percentages versus pixels; frameworks and templates; max width

MTA Exam 98-364: Database Fundamentals

Understand core database concepts

Create Database Objects

Manipulate data

Understand data storage

Administer a database

Understand core database concepts

Understand how data is stored in tables

Understand what a table is and how it relates to the data that will be stored in the database; columns/fields, rows/records

Understand relational database concepts

Understand what a relational database is, the need for relational database management systems (RDBMS), and how relations are established

Understand data manipulation language (DML)

Understand what DML is and its role in databases

Understand data definition language (DDL)

Understand how T-SQL can be used to create database objects, such as tables and views

Create Database Objects

Choose data types

Understand what data types are, why they are important, and how they affect storage requirements

Understand tables and how to create them

Purpose of tables; create tables in a database by using proper ANSI SQL syntax

Create views

Understand when to use views and how to create a view by using T-SQL or a graphical designer

Create stored procedures and functions

Select, insert, update, or delete data

Manipulate data

Select data

Utilize SELECT queries to extract data from one table, extract data by using joins, combine result sets by using UNION and INTERSECT

Insert data

Understand how data is inserted into a database, how to use INSERT statements

Update data

Understand how data is updated in a database and how to write the updated data to the database by using the appropriate UPDATE statements, update by using a table

Delete data

Delete data from single or multiple tables, ensure data and referential integrity by using transactions

Understanding data storage

Understand normalization

Understand the reasons for normalization, the five most common levels of normalization, how to normalize a database to third normal form

Understand primary, foreign, and composite keys

Understand the reason for keys in a database, choose appropriate primary keys, select appropriate data type for keys, select appropriate fields for composite keys, understand the relationship between foreign and primary keys

Understand indexes

Understand clustered and non-clustered indexes and their purpose in a database

Administer a database

Understand database security concepts

Understand the need to secure a database, what objects can be secured, what objects should be secured, user accounts, and roles

Understand database backups and restore

Understand various backup types, such as full and incremental, importance of backups, how to restore a database

MTA Exam 98-361: Software Development Fundamentals

Understand programming

Understand object-oriented programming

Understanding general software development

Understanding desktop applications

Understand web applications

Understanding databases

Understand programming

Understand computer storage and data types

How a computer stores programs and the instructions in computer memory, memory stacks and heaps, memory size requirements for the various data storage types, numeric data and textual data

Understand computer decision structures

Various decision structures used in all computer programming languages; If decision structures; multiple decision structures, such as If…Else and switch/Select Case; reading flowcharts; decision tables; evaluating expressions

Identify the appropriate method for handling repetition

For loops, While loops, do-While loops, and recursion

Understand error handling

Structured exception handling

Understand object-oriented programming

Understand the fundamentals of classes

Properties, methods, events, and constructors; how to create a class; how to use classes in code

Understand inheritance

Inheriting the functionality of a base class into a derived class

Understand polymorphism

Extending the functionality in a class after inheriting from a base class, overriding methods in the derived class

Understand encapsulation

Creating classes that hide their implementation details while still allowing access to the required functionality through the interface, access modifiers

Understanding general software development

Understand application life cycle management

Phases of application life cycle management, software testing

Interpret application specifications

Reading application specifications and translating them into prototypes, code, select appropriate application type, and components

Understand algorithms and data structures

Arrays, stacks, queues, linked lists, and sorting algorithms; performance implications of various data structures; choosing the right data structure

Understanding desktop applications

Understand Windows apps

UI design guideline categories, characteristics and capabilities of Store Apps, identify gestures

Understand console-based applications

Characteristics and capabilities of console-based applications

Understand Windows Services

Characteristics and capabilities of Windows Services

Understand web applications

Understand web page development

HTML, Cascading Style Sheets (CSS), JavaScript

Understand Microsoft ASP.NET web application development

Page life cycle, event model, state management, client-side versus server-side programming

Understand web hosting

Creating virtual directories and websites, deploying web applications, understanding the role of Internet Information Services

Understand web services

Web services that will be consumed by client applications, accessing web services from a client application, SOAP and Web Service Definition Language (WSDL)

Understanding databases

Understand relational database management systems

Characteristics and capabilities of database products, database design, Entity Relationship Diagrams (ERDs), normalization concepts

Understand database query methods

Structured query language (SQL), creating and accessing stored procedures, updating data and selecting data

Understand database connection methods

Connecting to various types of data stores, such as flat file; XML file; in-memory object; resource optimization

MTA Exam 98-349: Windows Operating System Fundamentals

 Understanding operating system configurations

• Configure Control Panel options

·        Configure administrative tools, configure accessibility options, configure power settings, configure File Explorer settings

• Configure desktop settings

·        Configure profiles, display settings, and shortcuts; configure and customize Start Menu; configure Task Bar settings; configure toolbars; configure notifications

• Configure native applications and tools

·        Configure Microsoft Edge, configure Cortana, configure Hyper-V, configure settings using MSCONFIG, configure processes and applications using Task Manager, configure computer management

• Configure mobility settings

·        Configure Sync Center, Windows Mobility Center, and Remote Desktop

• Configure and use management tools

·        Configure MMC, configure the Windows PowerShell console and Windows PowerShell ISE

Installing and upgrading client systems

• Identify Windows operating system editions

·        Identify hardware and compatibility requirements, determine appropriate editions per device type

• Identify upgrade paths

·        Identify upgrade paths from previous Windows versions, identify application compatibility

• Understand installation types

·        Perform a clean install, upgrade via Windows Update, migrate from previous Windows versions, perform removable media installation, perform network installation

• Understand operating system architecture

·        Understand kernel mode; understand user mode; understand memory, IRQs, drivers, CPUs, and UI; understand 32-bit versus 64-bit architecture

Managing applications

• Configure applications

·        Understand local versus network applications, configure desktop applications, configure app startup options, configure Windows features, configure Windows SmartScreen, configure application removal, configure Windows Store apps

• Configure user account control (UAC)

·        Understand standard user versus administrative user, understand types of UAC prompts and levels

• Configure antivirus settings

·        Configure Windows Defender and the Malicious Software Removal tool

• Understand services

·        Understand service start-up types, service accounts, and service dependencies

Managing files and folders

• Understand file systems

·        Understand FAT32, NTFS, and ReFS

• Understand file and print sharing

·        Configure File System permissions, configure Share Permissions, configure HomeGroup settings, configure print drivers, configure effective permissions, create shares, create mapped drives

• Understand encryption

·        Understand BitLocker and Encrypting File Systems (EFS)

• Understand libraries

·        Understand offline files, configure libraries, add multiple local locations to a library, add networked locations

Managing devices

• Connect devices

·        Connect, enable, and disable plug-and-play and Bluetooth devices; connect and disconnect printers; install third-party software for devices; install device drivers

• Understand storage

·        Understand disk types, security (encryption), storage device types (eSATA, USB, IEEE 1394, iSCSI, InfiniBand), and storage drive types (basic, primary, extended, logical, dynamic disk, VHDs); configure OneDrive use; optimize drives

• Understand printing devices

·        Understand local printers, network printers, print queues, print-to-file, and Internet printing

• Understand system devices

·        Understand video, audio, and infrared input devices; understand Device Manager

Understanding operating system maintenance

• Understand backup and recovery methods

·        Configure System Restore; configure a recovery drive; configure recovery boot options, such as Last Known Good, and various Safe Mode options; recover files from OneDrive

• Understand maintenance tools

·        Understand Disk Defragmenter, Disk Cleanup, Task Scheduler, and System Information

• Configure updates

·        Configure Windows Update options; implement Insider Preview, Current Branch, and Current Branch for Business scenarios; manage update history; roll back updates

Systems and software in "Searching" Movie

Searching is a 2018 American thriller. Set entirely on smartphones and computer screens. the film follows a father trying to find his missing 16-year-old daughter with the help of a police detective. After his daughter goes missing, a desperate father breaks into her laptop and social media to look for clues to find her.

Systems, Websites, Web Apps, Mobile Apps and Software using in Movie

Microsoft Windows XP

a personal computer operating system produced by Microsoft as part of the Windows NT family of operating systems. It was released to manufacturing on August 24, 2001, and broadly released for retail sale on October 25, 2001.

MSN Messenger

a discontinued instant messaging client developed by Microsoft for Windows. It connected to the Microsoft Messenger service while also having compatibility with Yahoo! Messenger and Facebook Messenger.

Apple Mac OS

previously Mac OS X and later OS X, Roman numeral "X" pronounced "ten") is a series of graphical operating systems developed and marketed by Apple Inc. since 2001.

FaceTime

FaceTime is a proprietary videotelephony product developed by Apple Inc. FaceTime is available on supported iOS mobile devices and Macintosh computers that run Mac OS X 10.6.6 and later. FaceTime supports any iOS device with a forward-facing camera and any Macintosh computer equipped with a FaceTime Camera.

Google

Google LLC is an American multinational technology company that specializes in Internet-related services and products, which include online advertising technologies, search engine, cloud computing, software, and hardware. Google was founded in 1998.

Gmail

Gmail advertising-supported email service developed by Google. Users can access Gmail on the web and using third-party programs that synchronize email content through POP or IMAP protocols. Gmail started as a limited beta release on April 1, 2004 and ended its testing phase on July 7, 2009.

YouTube

YouTube, LLC is an American video-sharing website headquartered in San Bruno, California. YouTube allows users to upload, view, rate, share, add to favorites, report, comment on videos, and subscribe to other users.

Yahoo

Yahoo! is a web services provider headquartered in Sunnyvale, California and owned by Verizon Communications through Oath Inc. The original Yahoo! company was founded by Jerry Yang and David Filo in January 1994 and was incorporated on March 2, 1995. Yahoo was one of the pioneers of the early Internet era in the 1990s.

Facebook

Facebook, Inc. is an American online social media and social networking service company based in Menlo Park, California. Its website was launched on February 4, 2004, by Mark Zuckerberg, along with fellow Harvard College students and roommates Eduardo Saverin, Andrew McCollum, Dustin Moskovitz and Chris Hughes.

Instagram

Instagram is a photo and video-sharing social networking service owned by Facebook, Inc. It was launched in October 2010 exclusively on iOS. A version for Android devices was released a year and 6 months later, in April 2012.

Tumblr

Tumblr is a microblogging and social networking website founded by David Karp in 2007, and owned by Oath Inc. The service allows users to post multimedia and other content to a short-form blog

Venmo

Venmo is a mobile payment service owned by PayPal. It allows users to transfer money to others using the service using a mobile phone app; both the sender and receiver have to live in the U.S. It handled $12 billion in transactions in the first quarter of 2018

Crowdchase

YouCast

MemorialOne

Mathematics: Geometry Topics

        - Elementry

*Lines, angles, and triangles 

*Lines in the plane

*Congruent triangles 

*Quadrilaterals

*Similar triangles 

*Trigonometry of the right triangle

*Area and Perimeter 

*Regular Polygons and circles

- Lines and circles in general forms

- Geometric transformations in the plane

- Lines and Planes in the Space

- Coordinate systems in the plane

*Rectangular cartesian coordinates

*Polar coordinates

- Coordinate systems in the space

*Cylindrical coordinates

*Sperical coordinates system

- Conic sections

*Hyperbola

*Parbola

*Ellipse

- Quadrics Surfaces

*Hyperbolid

*Parabolaid

*Ellipsoid

- Ruled Surfaces

- The Sphere