Must (subjective obligation)
We often use must to say that something is essential or necessary, for example:
I must go.
Structure of Must
"Must" is a modal auxiliary verb. It is followed by a main verb. The structure is:
subject + must + main verb
The main verb is the base verb (infinitive without "to").
Look at these examples:
Use of Must
In general, "must" expresses personal obligation. "Must" expresses what the speaker thinks is necessary. "Must" is subjective. Look at these examples:
I must stop smoking.
You must visit us soon.
He must work harder.
In each of the above cases, the "obligation" is the opinion or idea of the person speaking. In fact, it is not a real obligation. It is not imposed from outside.
We can use "must" to talk about the present or the future. Look at these examples:
I must go now. (present)
I must call my mother tomorrow. (future)
There is no past tense for "must". We use "have to" to talk about the past.
Must Not (prohibition)
We use must not to say that something is not permitted or allowed, for example:
Passengers must not talk to the driver.
Structure of Must Not
"Must" is an auxiliary verb. It is followed by a main verb. The structure for "Must Not" is:
Subject + "Must Not" + Main Verb
The Main Verb is the base verb (infinitive without "to").
"Must Not" is often contracted to "mustn't".
Look at these examples:
auxiliary "Must" + "Not"
NB: like all auxiliary verbs, "must" cannot be followed by an infinitive. So, we say:
You mustn't arrive late. (not You mustn't to arrive late.)
Use of Must Not
"Must Not" expresses prohibition - something that is not permitted, not allowed. The prohibition can be subjective (the speaker's opinion) or objective (a real law or rule). Look at these examples:
I mustn't eat so much sugar. (subjective)
You mustn't watch so much television. (subjective)
Students must not leave bicycles here. (objective)
Policemen must not drink on duty. (objective)
We use "Must Not" to talk about the present or the future:
Visitors must not smoke. (present)
I mustn't forget Tara's birthday. (future)
We cannot use "Must Not" for the past. We use another structure to talk about the past, for example:
We were not allowed to enter.
I couldn't park outside the shop.
Shall and Will
People may sometimes tell you that there is no difference between shall and will, or even that today nobody uses shall (except in offers such as "Shall I call a taxi?"). This is not really true. The difference between shall and will is often hidden by the fact that we usually contract them in speaking with 'll. But the difference does exist.
The truth is that there are two conjugations for the verb will:
1st Conjugation (objective, simple statement of fact)
I shall be in London tomorrow.
You will see a large building on the left.
he, she, it
He will be wearing blue.
We shall not be there when you arrive.
You will find his office on the 7th floor.
They will arrive late.
2nd Conjugation (subjective, strong assertion, promise or command)
I will do everything possible to help.
You shall be sorry for this.
he, she, it
It shall be done.
We will not interfere.
You shall do as you're told.
They shall give one month's notice.
It is true that this difference is not universally recognized. However, let those who make assertions such as "Americans never use 'shall'" peruse a good American English dictionary, or many American legal documents, which often contain phrases such as:
Each party shall give one month's notice in writing in the event of termination.
Note that exactly the same rule applies in the case of should and would. It is perfectly normal, and somewhat more elegant, to write, for example:
I should be grateful if you would kindly send me your latest catalogue.
Children have to go to school.
I must go to the university.
People mustn't drive a car when they drink alcohol.
I needn't do math today, I can do it later.
I should study harder before exams.
Elephants and mice can't fly.
I could play snooker much better two years ago than I can now.
I can't have made a mistake in my calculations because I used a calculator.
Can you run 100 meters in 5.5 seconds? 10)
Students mustn't eat or drink during the lection.
Specialists in a broad range of fields have to deal with problems that involve combinations made up of letters, numbers or any other objects.
The field of mathematics that studies problems of how many different combinations can be built out of a specific number of objects is called combinatorial mathematics (combinatorics).
This branch of mathematics has its origin in the 16th century, in the gambling games that played such a large part in high society in those times. These games gave the initial impetus to develop combinatorial mathematics and the theory of probability.
Italian and French mathematicians were the first to enumerate the various combinations achieved in games of dice. Further advances in the theory of combinations were connected with the names of German scientists.
In recent years combinatorial mathematics has seen extensive developments associated with grater interest in problems of discrete mathematics. Combinatorial methods can be employed in solving transport problems, in particular scheduling; the scheduling of production facilities and of the sale of goods. Links have been established between combinatorics and problems of linear programming, statistics, etc. Combinatorial methods are used in coding and decoding and in the solution of other problems of information theory.
The combinatorial approach also plays a significant role in purely mathematical problems such as the theory of groups and their representations, in the study of the main principles of geometry, some branches of algebra, etc.
Probability is a mathematical expression of the likelihood of an event. Every probability is a fraction. The largest probability can be 1. The smallest probability can be is 0, meaning that it's something that cannot happen. You can find the probability that something will not happen by subtracting the probability that it will happen from 1. For example, if the weatherman tells you that there is a 0.3 probability of rain today, then there must be a 0.7 probability that it won't rain.