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Introduction

The Importance of Mathematics in Computer ScienceMathematics plays a crucial role in computer science, serving as the foundation for many computational theories, algorithms, and practical applications. The connection between mathematics and computer science is so deep that a strong mathematical background is essential for success in various fields of computing. This article explores the importance of mathematics in computer science, highlighting key areas where mathematical concepts are applied and demonstrating how they contribute to advancements in technology.<h3>Mathematical Foundations of Computer Science</h3>Computer science is fundamentally built on mathematical principles. Theoretical computer science, which encompasses areas like algorithms, data structures, and complexity theory, relies heavily on mathematical reasoning. Some of the most significant mathematical disciplines that support computer science include:<ol start="1" data-spread="true"><li>Discrete Mathematics – Discrete mathematics provides the foundational concepts used in computer science, such as set theory, logic, graph theory, and combinatorics. These concepts help in designing algorithms, understanding data structures, and developing logical reasoning skills necessary for programming.</li><li>Boolean Algebra and Logic – Boolean algebra is essential in designing digital circuits and performing logical operations. Logical reasoning helps in constructing conditional statements and decision-making processes in programming and artificial intelligence.</li><li>Graph Theory – Graphs are widely used in computer science for modeling relationships and networks. Applications of graph theory include social networks, database indexing, networking algorithms, and artificial intelligence.</li><li>Linear Algebra – This branch of mathematics is crucial in fields such as computer graphics, machine learning, and data science. Linear algebra helps in manipulating large datasets and performing transformations in graphics rendering.</li><li>Probability and Statistics – These mathematical disciplines are vital in data analysis, artificial intelligence, and machine learning. Understanding probability and statistics allows computer scientists to develop predictive models, analyze trends, and optimize decision-making processes.</li><li>Number Theory and Cryptography – Cryptography, which ensures secure communication and data protection, is heavily dependent on number theory. Concepts such as modular arithmetic and prime factorization are used in encryption techniques that safeguard digital information.</li></ol><h3>Mathematics in Algorithms and Programming</h3>Algorithms form the backbone of computer science, and their efficiency is determined by mathematical analysis. Some key areas where mathematics influences algorithm design and programming include:<ul data-spread="true"><li>Time Complexity and Big O Notation – The efficiency of an algorithm is measured using Big O notation, which helps in understanding how the performance of an algorithm scales with input size. This mathematical analysis is critical for optimizing code and developing efficient software solutions.</li><li>Recursion and Induction – Recursion, a fundamental programming concept, is closely related to mathematical induction. Many complex problems, such as tree traversal and dynamic programming, rely on recursive approaches for efficient problem-solving.</li><li>Optimization and Linear Programming – Optimization techniques help in finding the best possible solutions to problems by minimizing or maximizing a certain objective function. These techniques are widely used in artificial intelligence, machine learning, and logistics.</li></ul><h3>Mathematics in Emerging Technologies</h3>With the rise of artificial intelligence, machine learning, and big data analytics, the role of mathematics in computer science has become more pronounced.<ul data-spread="true"><li>Machine Learning and Artificial Intelligence – These fields rely heavily on statistical models, probability theory, and linear algebra. Understanding the mathematical principles behind neural networks, deep learning, and data modeling is essential for developing intelligent systems.</li><li>Computer Vision and Image Processing – Techniques such as Fourier transforms, matrix operations, and statistical analysis are used to process and interpret visual data. Applications of these mathematical concepts include facial recognition, medical imaging, and augmented reality.</li><li>Blockchain and Cryptographic Security – The security and integrity of blockchain technology depend on cryptographic algorithms, which are based on complex mathematical principles such as elliptic curve cryptography and hash functions.</li></ul><h3>Conclusion</h3>Mathematics is the backbone of computer science, providing the theoretical and practical tools necessary for solving computational problems. From algorithm design to artificial intelligence and cryptography, mathematics is deeply intertwined with every aspect of computing. A strong foundation in mathematics enhances problem-solving abilities and allows computer scientists to develop innovative and efficient technological solutions. As computer science continues to evolve, the significance of mathematics will only grow, reinforcing its critical role in shaping the future of technology.

Mykola G.

Unlocking the Secrets of English Grammar: Your Path to Fluent Expression

Sеction 1: Thе Grammar Mazе Unvеilеd Imaginе English grammar as a mystеrious mazе that you'rе navigating blindfoldеd. In this sеction, wе'll rеmovе that blindfold and shеd light on thе fundamеntal principlеs that govеrn our languagе.
Subsеction: Thе Sеntеncе Structurе Sеcrеt Unlock thе powеr of constructing clеar and concisе sеntеncеs. Wе'll еxplorе subjеcts, prеdicatеs, and еvеrything in bеtwееn. No morе tanglеd sеntеncеs; it's timе for clarity to shinе.
Sеction 2: Tackling thе Common Offеndеrs Evеr cringеd at thе misusе of "your" and "you'rе"? Or pеrhaps you'vе pondеrеd thе еnigma of "its" vеrsus "it's." In this sеction, wе'll confront thеsе notorious grammar offеndеrs hеad-on.
Subsеction: Homophonеs Dеmystifiеd Discovеr thе world of homophonеs - words that sound thе samе but havе diffеrеnt mеanings and spеllings. Gеt rеady to wiеld thеsе linguistic wеapons with prеcision.
Sеction 3: Thе Art of Punctuation Punctuation marks arе thе unsung hеroеs of writing. Wе'll еxplorе thе subtlе yеt transformativе rolе thеy play in shaping your prosе.
Subsеction: Thе Mighty Comma Unlock thе potеntial of thе comma, thе tiny warrior that can changе thе еntirе mеaning of a sеntеncе. Lеarn whеn to pausе, whеn to connеct, and whеn to lеt your words flow.
Sеction 4: Avoiding Grammatical Pitfalls In this sеction, wе'll navigatе thе trеachеrous tеrrain of grammar pitfalls. From thе pеrils of doublе nеgativеs to thе confusion surrounding irrеgular vеrbs, wе'll conquеr thеsе challеngеs togеthеr.
Subsеction: Thе Doublе Nеgativе Dilеmma Divе dееp into thе world of doublе nеgativеs and lеarn how to avoid thе pitfalls that can turn your sеntеncе into a linguistic abyss.
Sеction 5: Thе Road to Mastеry Wе'vе journеyеd through thе labyrinth of English grammar, and now it's timе to еmеrgе as conquеrors. This sеction providеs you with tools and stratеgiеs to mastеr grammar.
Subsеction: Bеcoming a Grammar Guru Transform yoursеlf into a grammar guru by practicing what you'vе lеarnеd. Engagе in еxеrcisеs and quizzеs that will solidify your knowlеdgе and boost your confidеncе.
Section 6: Writing with Flair Beyond mastering grammar rules, writing with flair adds depth and impact to your communication. Explore techniques to infuse creativity into your writing.
Expressive Vocabulary: Dive into the world of vivid vocabulary. Learn how to select words that paint vibrant pictures and evoke emotions in your readers.
Captivating Style: Discover different writing styles and their effects on your audience. From persuasive to narrative, find your unique voice and captivate your readers.
Section 7: Crafting Compelling Content Understanding grammar is just the beginning; crafting compelling content elevates your writing. Uncover the secrets of engaging your audience through captivating content.
Storytelling Techniques: Explore the power of storytelling in writing. Learn how to weave narratives that resonate, inspire, and leave a lasting impact.
Engaging Introductions and Endings: Master the art of crafting captivating introductions that hook your readers and endings that leave a lasting impression.
Section 8: The Revision Process Writing isn't just about the first draft; the magic often lies in revisions. Discover how revising and editing can transform your work from good to exceptional.
Effective Editing: Learn techniques for effective self-editing. Understand how to refine your work, cut unnecessary clutter, and enhance clarity.
Feedback and Improvement: Embrace the value of feedback. Discover how peer reviews and constructive criticism can elevate your writing to new heights.
Conclusion: Congratulations, bravе grammarians! You'vе travеrsеd thе grammar mazе, unеarthing its sеcrеts and wiеlding its powеr. Armеd with this nеwfound knowlеdgе, you'rе now еquippеd to еxprеss yoursеlf fluеntly and writе with confidеncе.

Medhat A.

Top 3 Common Business English Expressions

Top 3 Common Business English Expressions
A few months ago, I had the pleasure to have a conversation with the ESL teacher, Business English Coach, and Ph.D. in Germanic Languages Uliana Tykha. We talked about her Instagram blog, business English, ESL, methods of improving English, useful English expressions, and teaching English online.
In this abstract, I would like to share with you 3 English business expressions which we discussed with Uliana. 
– Uliana, I know that you are a business English teacher, so could you share with us the top three business English expressions? 
– There are so many of them that I really like, but the ones that I would like to share with you today will be the first one:
<ol style="text-align: justify;">
<li>To make a killing, which means to get great financial success, so we can say that the company made a killing on this retail project.</li>
</ol>
– I heard this expression. It's probably like “to break the bank”. 
– Yes, to have a breakthrough in business, yes, to have great financial success.
– Unfortunately, I didn't make a killing because I was afraid and withdrew my money from Bitcoin, and Bitcoin skyrocketed. How stupid I was. I didn't make a killing.
– Yes, this is a risky business to invest yes all your savings in some digital currency.
– Yes, but we say: “who doesn't take a risk, that doesn't drink champagne”.
– It would be nice to know how it sounds in English, maybe they have some good alternative to this expression.
– Yeah, that's right, maybe the similar expression is “hit or miss”.
– So another one is rather informal, but I really like it.
<ol style="text-align: justify;" start="2">
<li>To go belly up means you can imagine when something goes belly up. So basically it fails, or the company goes bankrupt. You can imagine it like an animal is dying, they're going belly up. So this is the origin of this expression. It means to fail or to go bankrupt. </li>
</ol>
– This expression is when some fish can go belly up, a fish or turtle, but this is associated with the kind of cockroaches. 
– You can say that a lot of businesses have gone belly up during this pandemic, maybe some restaurant chains.
– Yes, and things like catering businesses went belly up. However, delivery businesses are making a killing.
– Yes, for sure, definitely yes. Okay, and number three is to talk shop. 
<ol style="text-align: justify;" start="3">
<li>To talk shop means to discuss something related to your work, some matters related to your work when it is not quite appropriate when you're outside your work where you're not in the office. So you can be talking about your job when people are not interested in that and say, Mark, stop talking shop, we are not in the office. </li>
</ol>
– Yeah, something like that, and we would say: “oh, good for you” (laughing).
– It means to annoy a person by always discussing your business-related matters, maybe at home, maybe among your friends. This is to talk shop. These are the expressions that I really like, but there are so many of them, you can check them up on my Instagram page of course. 
– As far as I know, you are a business English coach for some successful international companies. What are your methods of teaching business English, and what does your business English class look like?
– So I would say at the beginning that I'm trying to focus on the specific needs of my clients or students and some learning outcomes because there are so many requests from them: some people speak English, but they need English as a means to achieve some specific career-related goals, for example, they need to communicate in English in their work environment.  Someone is looking for a job and needs to have an interview in English. Some people are traveling and having these business trips, and they need to be able to communicate in this international business environment, to have this business small talk, things like that. Some people, like managers at some companies, need English to get some customers or clients from abroad. I tried to design our recessions, basically to customize the sessions to meet these specific needs and, of course, apart from this, functional language and this specific business vocabulary we're also trying to develop the awareness of different communication strategies in business, to develop an awareness of some communication issues like building rapport, some customer service communication managing conversations and so on, and also we are developing some important business skills like negotiating, presenting ideas resolving some conflicts, things like that, so English as a means of communication in an international business environment. And on top of this, we are also discussing a lot of realistic business cases, so with all these things integrated into our sessions, these business people have excellent results, and I'm very happy when they give me their feedback and say to me that I was abroad, and I'm extremely happy when they give me this feedback and um tell me that, for example, they managed to get some clients from abroad that they were extremely difficult to reach out to because of some lack of you know professional business communication and our recessions really brought them a lot of value. So this is basically how it works, and I'm really enjoying it.
– Thanks a lot, Uliana. It was nice to talk to you! 
– It was nice to talk to you, too, Mark! You are welcome!

Mark T.

Top 4 Common IT Terms in English

Top 4 Common IT Terms in English
Not so long time ago, I had an exciting talk with Mykhailo Seniutovych who is a professional Ukrainian programmer, great traveler, and dancer. 
I kindly asked him to share with us some common IT terminology programmers use at work. 
– Mykhailo, since you are a professional programmer, could you give us some useful words or collocations or maybe idioms that would be helpful for English learners and for programmers as well?
– I guess the first thing, probably you heard about it, it's called a bug. 
<ol style="text-align: justify;">
<li>Bug. So if the program doesn't work properly right, if its functionality is broken, we call that a program has a bug. So this program is so hard to use because it has so many bugs. There are many meanings of the word “bug” but probably this is not the primary meaning here. That's why I want to give you a story about why it's called the box, so a bug is this small insect that we probably all know of beetle. I think it's a synonym. So why is it called the bug? Back in the 1950s when those first computers were created, those first computers were huge, they took up whole rooms that were taken by computers and once one of those computers didn't work, and they didn't understand what was going on they started to look inside the computer, and they've literally found a bug in the inside like this insect little animal. From that point on they started to call like when some malfunction happens, they would say it's a bug, but that's where it came from, which is an interesting story. </li>
</ol>
– There is another meaning to the word “bug”. Probably someone is bugging us. It means they have a bug and if it's our private conversation and someone can be bugging us. So, it’s the third meaning of the word “bug”.
– Yeah, that's good to know. Well, I am talking about the context of programming, and if we talk about this word bug, you can there is also another word to debug. 
<ol style="text-align: justify;" start="2">
<li>Debug. I need to debug a program and usually, it means that you sort of need to examine the code you sort of run the program slowly kind of line by line, and just see where the problem is where this bug is, so you debug your program. </li>
</ol>
– Well, maybe the explanation would be to identify a bug?
– It's more or less a good explanation, but sometimes you debug a program just to understand how it works better. So it can be used in this context, but “debug” is like the thing that every programmer does and everyone knows.
– Alright, so what’s the next one?
– The next one is a feature. 
<ol style="text-align: justify;" start="3">
<li>Feature. You probably know this word, but in the context of programming, we say that if the program has some rich functionality, like on Facebook, let's say you can send messages to many people at once. So we can say Facebook has a feature to send more multiple messages to multiple users. It's a piece of functionality that the program has and usually when we, as programmers, create our programs, we create a list of these features that the program should have. So in the context of Facebook that would be like you can send messages to one user, send messages to many users, can add friends, and all of these things. These all would be features. </li>
</ol>
– What about in everyday life because I think that the feature has a lot of other meanings?
– Yes, you tell me, you're the English teacher here (laughing). 
– Well, I'm an English teacher with a feature, with many features. So I can talk, I can hear, I can read, I can listen, I can write. It can also be facial features. Probably in this context, everybody knows the word “feature”.
– Yeah, so it's pretty much similar in the context of programs, but it's just something that we use all the time when we write our programs. There is always work like what features this program should have. So it's a very commonly used word among programmers. 
<ol style="text-align: justify;" start="4">
<li> Deploy it to production. And the last one that I've got is what you do when you write your code, you write a program, and then it's ready to go live and for users to use it. When that happens, we say we deploy it to production. So “to deploy” means to kind of like place it somewhere. That's what the word “deploy” means: to place it at some place, and we say “to production” because this is a production environment so usually when we write programs there are different environments. There is a test environment, so the test environment is where the program is being tested. So if I just created some program, but I'm not sure if it works well or badly, I usually give it to testers, but it would not be available for every user, it would be available only for people who will test this program and once they test this program, it's good it works fine. Only then do we release it. So we deploy the program to production, and again that's a thing that is used very often if your program can be deployed.</li>
</ol>
– Thank you, Mykhailo, for such a fruitful conversation!
– You are welcome!

25 Common Collocations with "Go" without Prepositions

25 Common Collocations with "Go" without Prepositions
The collocation is a group of 2 or more words that usually go together.
Today, let’s have a look at 25 collocations with “go” without prepositions:
<ol>
<li> Go bald – lose one’s hair</li>
</ol>
   E.g. He’ll probably go bald in his thirties, as his father did.
   Unfortunately, some of my friends started going bald at 25 and were completely bald by 35.
   I think nobody wants to go bald at a young age.
<ol start="2">
<li> Go insane – become mentally ill; to go crazy – often used in an exaggerated way.</li>
</ol>
   E.g. If he doesn’t stop yelling like that, I’m going to go completely
   insane/crazy!
   I sometimes think I’m going insane (= I feel very confused)
<ol start="3">
<li> Go missing – run away, disappear, vanish, become lost or absent</li>
</ol>
   E.g. The train went missing in the smog.
   My jewelry has gone missing, and I want to call the police!
   – How did the cat go missing? – I have no idea!
<ol start="4">
<li> Go overseas – go abroad</li>
</ol>
   E.g. You have to be over 18 to go overseas in this country.
   Internships allow bright students to go overseas and gain experience
   In leading universities.
   We don’t need to go overseas to meet people who don’t care about
   The environment.
<ol start="5">
<li> Go bankrupt – be unable to pay one’s debts; have no money</li>
</ol>
   E.g. That company went bankrupt/went broke.
   Jack went bankrupt/broke after just 2 years in business.
   The lockdown has led to lots of businesses going bankrupt.
   I’ll go bankrupt with such a wife like you are!
<ol start="6">
<li> Go out of business – stops doing business permanently, especially</li>
</ol>
   Because it has failed; not in working order, inoperative
   E.g. If you give everything for free, we’ll soon go out of business.
   John went out of business when he turned 35.
   The slot machine seems to be out of business tonight.
<ol start="7">
<li> Go astray – go away from the correct path or correct way of doing something; become lost</li>
</ol>
   E.g. The parcel might have gone astray in the mail.
   A lot of items of the post being sent to him have gone astray.
   I guess my suitcase has gone astray. Somebody might have taken it
   By mistake.
<ol start="8">
<li> Go bad – become spoiled; some food is not fresh enough to eat or drink; become unpleasant or unfavorable; begin to engage in some illegal matters.</li>
</ol>
   E.g. It seems that the jam has gone bad. You need to throw it away.
   They can’t speak with each other anymore. Their relationship has gone bad.
   They always seem so annoyed with each other. I bet their relationship
   Has gone bad.
   If that student continues being a friend of those criminals, he will go bad.
<ol start="9">
<li> Go home – go to your place</li>
</ol>
   E.g. If you have nothing to do, just go home.
   I’m so tired. Let’s go home.
   One can’t travel so long. Sooner or later they’d like to go home.
<ol start="10">
<li> Go downtown – go to the central part of the city; be arrested or go to jail.</li>
</ol>
   E.g. You might want to go downtown with me. I’m bored staying at home.
   If I were you, I’d go downtown to watch an interesting gig.
   George went downtown after being caught robbing the bank.
<ol start="11">
<li>Go north, go south, go west, go east</li>
</ol>
    Would you rather go north or go south?
   You’d better go west than go east. 
   “Go west” is a good song by “Pet Show Boys”.
<ol start="12">
<li> Go viral </li>
</ol>
   If a video, image, or story goes viral. It spreads quickly and widely on the internet through social media and email.
   E.g. His video went viral with 100 million views. 
   What should he do to make his video viral? 
   I can’t believe that the video with the fluffy cat went viral. 
<ol start="13">
<li>Go straight – Literally, to move forward in the direction one is facing.</li>
</ol>
   E.g. Just go straight, turn left, and you’ll see the shop. 
   Slang To begin to respect the law after a period of crime.
   At last, he started to go straight after spending 10 years in prison. 
   Slang To stop taking drugs.
   If you don’t go straight, you’ll get addicted to those kinds of drugs really fast. 
<ol start="14">
<li>Go left – go to the left side,</li>
<li>Go right – go to the right side</li>
</ol>
   E.g. Go left, then go straight, and then go right, and you’ll see me standing near the University. 
<ol start="16">
<li>Go up  1. To increase.</li>
</ol>
   E.g. Car prices have gone up abruptly, so probably we’ll sell our car.
   If the temperature goes up to 30 degrees Celsius, we’ll have to buy an AC. 
<ol start="2">
<li>To walk over or up to something.</li>
</ol>
    E.g. Please go up to me, and I’ll show you how to fix your device. 
    I'll just go up to the salesman and ask how much this vacuum costs.
<ol start="3">
<li>To climb or ascend something.</li>
</ol>
    E.g. His dad went up the ladder, wasn’t careful, and fell down.
<ol start="17">
<li>Go down. 1. To lower, sink, or fall.</li>
</ol>
    E.g. After the sun goes down, we should throw a party!
    Shares in the company went down after Chinese sanctions. 
<ol start="2">
<li>To occur, happen, or unfold, as an event or action.</li>
</ol>
    E.g. We need to clarify what went down there before we change our strategy. 
<ol start="18">
<li>Go shopping means that your intentions are to buy things or purchase new versions of something. </li>
</ol>
   E.g. You need to go shopping for a new dress. 
   She likes to go shopping on the weekend. 
   We went shopping for some presents at the mall
<ol start="19">
<li>Go running – go jogging</li>
</ol>
   E.g. Let’s go running. The weather is awesome. 
<ol start="20">
<li>Go swimming – to have intentions to swim </li>
</ol>
   E.g. If I were you, I’d definitely go swimming.
<ol start="21">
<li> Go snowboarding – to ride on the snowboard</li>
</ol>
   E.g. I would rather go snowboarding than staying at home.
<ol start="22">
<li>Go skating – to ride on skates</li>
</ol>
   E.g. When I was younger, I would go skating.
<ol start="23">
<li> Go dancing – to dance with someone</li>
</ol>
   E.g. I’d like to go dancing with you. 
<ol start="24">
<li>Go skiing – to hit the slopes</li>
</ol>
   E.g. Going skiing is often dangerous.
<ol start="25">
<li> Go fishing – to go somewhere to catch fish</li>
</ol>
 E.g. When was the last time you went fishing? 
Write down your 5 examples with the collocations without prepositions in the comments below.

Priceless Tips on Improving 4 Language Skills for the IELTS 

Priceless Tips on Improving 4 Language Skills for the IELTS 
Lately, I’ve had an interesting interview with one of the best English teachers in Pakistan, a TESOL Certified Instructor, M.A. in English language and literature in 2 universities: Arizona State University and the University of Karachi Kashif Hussein. We talked about how to master the English language quickly and how to prepare for the IELTS very well.
– Many people are leaving their countries and taking the IELTS (General or Academic). How do you study your students for the IELTS? What methods do you use? Do you teach English by the book or do you have your own program?
– I really appreciate this million-dollar question, and most IELTS students keep searching for that answer from experts. I would like to take your two minutes in order to give the answer to this question as this is something which I need to elaborate on right well. 
Concerning the IELTS, there are four skills that the British Council and other examination bodies take the test: reading writing, speaking, and listening:
<ol style="text-align: justify;">
<li>Reading If I talk about reading first, so in reading there are different materials that we have available in our surroundings. It’s also worth mentioning that if you want to improve your spoken skills, so you need to read different articles, newspapers, blogs magazines research papers, etc. right. This is one of the most significant things that you can do for the reading. Another one is that the reading should be for understanding. Reading should not be for the sake of reading. Reading should be for the sake of understanding, and in order to read some articles try to go for the plethora of reading. If you like novels, dramas, fiction or non-fiction stories, or you can say research papers, economic conditions, economical articles, whatever you want to read, just try to read it out.</li>
<li>Writing. Another one is writing, which is one of the most important things in which most people face difficulty in learning and preparing for the exam. So for the writing, I always suggest my students write an essay about their lives first. It has certain steps that they have to follow:</li>
</ol>
<ul style="text-align: justify;">
<li>the first step is to write about your daily routine to write about your friends family members your business, about your office colleague; </li>
<li>another one is if they want to get excellence in writing, so they must write, they must go for academic writing. There are certain topics that we have here like nowadays. COVID is very in, many writers are writing on it, and if you want to get a space in writing, so you can go for the burning topics that are very-very common in this era.</li>
</ul>
<ol style="text-align: justify;" start="3">
<li>Speaking. Another one is speaking. You must speak as much as you can. Don't worry about the grammar at the very first stage. At first, try to make yourself habitual of spoken English whether you're talking with natives or non-natives you're talking with your friends, colleagues, or anybody, just try to have a conversation with them on a daily basis, as this is something which requires high concentration. So you need to go for this thing.</li>
<li>Listening. In order to improve your listening skills, you can go for listening to clips. There are certain clips that are easily available on Google on different search engines, so you can quickly jump on that and try to find out the best listening audios for yourself, and side by side you can solve some exercises which can be helpful for you in order to practice listening skills. </li>
</ol>
So that's how I usually prepare my students for the IELTS exam. There are certain other steps that I take for the students' requirements because the students are not the same. Some students are good at writing, some are good at reading some are good at speaking, but there is room for improvement. So I just try to fill that gap which I personally believe that students must need it. 
– Do you give them any connectors or linking words for better writing or speaking better, or how can they enhance the level of their vocabulary, and how do you estimate uh like whether it's a fancy word or it is a low-lexis word or high-lexis word? How can you wait how to improve your vocabulary?
– Vocabulary. For the IELTS exam, in order to improve or enhance your vocabulary, first, you need to read. All four skills are interconnected with each other. If you start reading, you will come to know how the words are usually utilized in the sentences. You can see enhancing vocabulary. You must go through different reading passages because the best source of getting vocabulary is from the reading passages and yes, I want to mention here one important thing about vocabulary if you really want to learn vocabulary, so just start with one word and try to find out what is adjective of that word adverb, preposition, conjunction or interjection, what are the other parts of the speech of the same word. Furthermore, you just do not need to learn one single word and try to use it, rather you should go and try to check out what the other words are similar to the same family, some syllables, maybe we have to find some synonyms and attributes. For example, if it's “good”, so we have to understand the coloring of this word. Sometimes, this synonym can be in different contexts and the different connotations, for example, it could be “wonderful” but “good” can also be “delicious”, so we have to understand that some context as well as that you need to learn the different adjectives of the same thing. For example, if I talk about “big”, “enormous” and “massive” are giving you close meanings, so you can use them in different ways, but the sentence would give you the same sense.
– Thanks a lot, Kashif, for such professional tips.
– You’re welcome!

"Learning a poem, memorizing words in any language is quick and easy."

People find it hard to remember Korean words because they are different in sound and structure from their native language. Learning and memorizing Korean words can be a lot of fun and easy! Not to mention the fact that Korean is very interesting. 
Have you ever studied a list of words in a new language and seemed sure you knew them, but when it's time to remember the words in a real-life conversation situation, you couldn't remember the word? Learning to remember is considered much harder than recognizing, but it doesn't have to be that way. World record holders in memory competitions have even claimed that people with an average IQ can easily use the same memory techniques and mnemonic tools to win world records themselves. In this blog, I'll present you with a story through which you'll improve your memorization of common Korean words. 
These strategies will help you learn how to memories words that are key to learning to speak Korean or any other language. Relying on memorization to learn vocabulary is difficult and often not fun! Korean words and sounds can sound meaningless to speakers of other languages. Note, repeating words over and over in your head won't help you learn the words properly. They can be memorized, but when the time comes to remember them, you will forget them. 
One of the most common methods that those who learn a language use is that they try to make it memorized by repeating it by heart. For example, imagine that on your list of words to memories is a Korean word (ireum | "name"). A typical student might just repeat this word over and over in his or her head. Although this may be successful in better memorization, it is impractical because: 
1. It takes an inordinate amount of time. 2. No deep connections are formed in the brain to recall the material learnt. Remember the winged phrase: "A picture is worth a thousand words". It really is true. Let's try comparing your brain's ability to remember picture details with its ability to remember the same details verbally, and you will notice that the brain can remember visual cues much more easily. The fact is that it takes less time to write down a word than it does to sit down, make an association and create a visual image. 
Visual images greatly reduce learning time, although their creation is also time-consuming. The technique involves creating mini-movies in your mind. You have to train your brain to create visual images for the information you are reading, by doing this a much deeper association is created. It is like reading a book rather than watching a film. When you read a book, your mind is forced to create visual images for the information you are reading, and you create much deeper associations in your mind. However, when you watch a film, the action is much more passive, because the director has already imagined what things should look like and shows it visually.
In this sense, using different processes to learn words is like reading a film script! You can imagine for yourself what is going on. Consequently, the process becomes more powerful if you create your own stories. How do you learn a poem by heart? As with many things in life, there is no definitive way to learn a poem. The way you remember things will be different from the way other people remember things. Your memories may be full of color, while someone else will remember sounds vividly. 
You may like lists, while someone else prefers pictures. One thing that the best memorizers agree on is that the more avenues you take for your memory, the better your recall will be. So, what should you do? One simple tip is to learn poems with your family. Why? Because when you study a poem with your family, you can more easily appreciate the ideas, emotions, language and points of view that you are expressing. Learning poems as a family, especially with young children, makes them stay in the children's brains for life! Also, memorizing poems helps everyone learn the complex intricacies of the English language by providing new terms or showing complex syntax! Top tips for remembering a poem 1. Be strategic. Choose a poem with pictures, sketches, patterns - it's much easier to learn a free verse by heart. 2. Do as you have done before. Rewrite the verse several times - on real paper. 3. Every time you try to learn something, be in tune with yourself 4. Be relentless 5. Be patient, success does not come overnight. You have to practice! 6. Be amazing, don't be afraid to develop your own verse learning plan, the main result. 
Once, a very interesting story happened to one of my students. He was in 7th grade, and he had a task for the week, to learn a poem. Since my student was confident in his abilities, he unashamedly put it off until the last minute until he said: "Oh s***, I've got homework!" and searched frantically for a poem that had the minimum number of words needed to pass. And then he tried desperately all night to learn the poem by heart, but all to no avail. But one morning, as he was being driven to school, he had a brilliant idea which he shared with everyone. A melody! You may ask what a melody has to do with it! It's simple! During the first period, he hummed quietly in one of his math’s lessons until he turned the poem into a song. And then he could even sing it in his sleep! When his name was called, he proudly stood on the podium in front of all his classmates and recited his poem. "Hope and skill are a thing of feathers. Turn the poem into a song. See if it really works. Just don't sing it in front of the whole class! So, I hope that my tips will help your children in their studies. You will no longer spend hours studying a poem or preparing an essay.

tutor_7193 .

“How to help a child with homework in English, Ukrainian”.

I think we've all had that moment in our lives when we realize that we can't bring ourselves to study well, to do the tasks we're given at school or university. And today I am going to tell you how you can fight this. 
The first step is to find a reason why you don't want to study, it must be a good one. Even if you don't think it is, it could be an aversion to the process of learning, a dislike of a particular task. For example, an aversion to mathematics and a desire to do something more enjoyable. By identifying the reason, you can choose the right strategy. Motivate yourself and if you find a reason why you are too lazy to study, try to eliminate it and continue to succeed. 
The next step you should go to is to find your motivation. Set yourself some kind of goal for what you want to learn well, to learn some new material or something else. It's no surprise that you don't want to learn without a proper incentive, because our brains are built in such a way that we all need some kind of motivation. Think about what you can achieve through learning... It could be a dream job, a good income and more. 
Third step: subscribe to motivational bloggers, watch videos like these that talk about productivity, planning, start a diary. I am always very motivated when I see other people studying, watch some notes on the same blogs or when I just agree with my friend that we study English together every day. She learns and I learn too. We kind of follow one another. If she is lazy, I motivate her and if I am lazy, she motivates me. A tandem works very well! 
Fourth step: I can advise you to pick up some very good stationery that will motivate you to study, make your desk cozy, put candles on it. Personally, this motivates and inspires me very much, let it be a certain ritual, when you come from school or university to sit down to do your homework, light candles, turn on your lamp, sit at your desk and start working. Find good notebooks and pens. Try to decorate your notes beautifully, so that you feel good about looking at them. Write down all your assignments in the notes or diary that you are given at school, that way you will not forget about them and you will do everything on time. Studies show that people who know in advance what they want to be in the future learn much better because they have a goal. When I was at school, I had no idea what I wanted to be, I didn't know what I was capable of. I thought everything was completely useless! And I thought I didn't have any talents. But then I realized that I really enjoy learning and teaching foreign languages. I realized that I am a versatile person and I like everything to do with communication. When I had to take some important exams, important papers, I always wrote everything down in my diary. Every day I had a weekly plan, not once did I miss anything, I handed everything in on time and so I had no further problems. When all the debts just pile up on you and more and more now 3 72 tomorrow. 
Never do difficult or unpleasant tasks first. Because the object of the desire to do anything, later on, will be lost. Always leave difficult tasks to the very end and don't get bogged down in doing one thing, concentrate on it, motivate yourself, think of rewards for stages of work or for the production as a whole, as you feel more comfortable. Try to focus on the rewards and not on what's in between. Enthusiasm grows and the work doesn't seem so dull and moody. 
I know there are some bloggers who say that studying at school and university is unnecessary. In fact, that's not true at all! Learning is necessary! It is important, believe me there is a difference between people who have graduated from university and those who have only completed secondary education. And, most importantly, you need to spend at least one evening just devoting it to yourself, like a Saturday or a Sunday. Watching your favorite videos, taking a bath, reading your favorite book or watching some interesting film or series, just learn not to think about school or university or exams, but devote the day to yourself. Try to go for a walk with friends or just with some nice people to the ice rink, to the cinema, to a cafe, to go shopping. It's really good for unloading your brain! 
Don't forget to go to bed on time. Ideally you should get 8 hours of sleep and establish a regular sleeping routine. It's better to go to bed earlier and wake up earlier. I suggest, for example, studying a textbook today, reading tomorrow, and watching a TV series the day after tomorrow, if you enjoy it, if it is not a drag, take breaks, e.g., set aside three days a week for reading. Find a hobby, draw, have fun! I hope my advice was useful to you, and that you got at least a small dose of motivation to learn - good luck to everyone!

How to start learning Chinese!

What is waiting for those who are ready to learn Chinese? Frequent meditations? Tea ceremonies for relaxation? Exotic food consumption? Perhaps a calligraphy? We will not exclude the above-mentioned cases, but we will start with the other! First of all, let's identify which "Chinese" we will study? There is a strong force of dialects, but the only official language of China is 普通话 or Putonghua, or mandarin. Mandarin is understood by all citizens of China and is the best language for communication. 
Now we know that we are going to learn the Mandarin! What can we expect in the first lessons? The first stage - learning Chinese transcription and pronunciation. No, nobody will make you read hieroglyphics right away, it is physically impossible! Fortunately, there is a special phonetic system for learning Chinese. This system is called 拼音. It is based on the standard Latin and English forms, so we can write and read each Chinese word with the help of it. It's easier now, isn't it? Of course, there are also a lot of variations, rules, and exceptions, but your teacher will easily explain all the complexities. Thus, you will be able to read Chinese words and even speeches right away.
The second stage is the study of tones. Chinese is a tonal language, and tone plays a great role in communication. Bad news - the wrong tone changes the meaning of the word (sometimes dramatically), good news - there are only four tones! This is how they are called: first, second, third and fourth tones. Here, without a teacher, it is already very difficult. You need to learn all the tones, and correctly represent them. This requires practice and correctly selected exercises. It is necessary to listen and interpret a lot of audio-files and try to imitate your teacher and speaker. Don't be afraid of tones, they are not as difficult as they look. In a couple of lessons, students are confident enough to read with tones.
The third stage is studying with educational materials. Teaching materials include textbooks, presentations, games, videos and even educational software. It is important to tell the teacher your goals. Why do you want to learn Chinese? Do you work with Chinese partners or are you planning to live and work in China, or do you like to travel, or are you just a fan of Chinese culture? Your goals set the tone for the whole scheme of study! Understanding your motivation, your teacher will create a unique and individual program, and you will immediately be able to practice the necessary and relevant vocabulary.
The fourth step is one of the most important... Homework! Completing your homework is 50% of your success. Do your homework, repeat the material, and ask the teacher if you can't understand something. Remember: it is very important to love Chinese and not to treat it as a punishment! 
The third step - feel the flow! Determine your own motivation and interests. There is no right or wrong ways to learn Chinese. Do not limit yourself in any way. Everything you see, read, and learn has a tremendous effect. Let Chinese become your favorite hobby and an enjoyable experience. In my opinion, the most important thing is not to lose interest or burn out. Make your pace of learning comfortable for you, do not wait for quick results, and you will see that they will indeed quickly appear.
This is how my Chinese classes are organized. I wish success to all those who have accepted this challenge and are committed to the goal. Do it more often, find topics that interest you, and improve your own motivation!

Alex R.

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