Discrete Structures and Theory of Logic (DSTL) Unit Four notes: AKTU B.Tech students
"Agar aap log DSTL (Discrete structure and theory of logic) ke Unit 4, jo ki Algebraic Structure h uske Handwritten notes dhundh rhe ho toh tension not because notes aaj ke time pr dhundhna apne aap mai ek mehnat ka kaam h aur adhe se jyada bachhe sirf isi tension mai rhte h ki unko khin se handwritten notes available ho jae jisse wo apni pdhai ko ek achhe level tk le ja ske aur ye bohot tension lene wali baat nai h kyuki handwritten notes aaj kl hr jagah available h. Usi tarah hmari website College material pr bhi aapko sabhi subjects ke notes, previous year question paper and also important questiones pdf available ho jaengi aur usi ke sath hmari team future jobs se related bhi blog post krti h. if you want ki aapko saari important and jobs related information jldi se jldi mile toh aap hmara whatsapp channel bhi follow kr skte h jiski link aapko page ke end mai milegi. us link pr click krke aap hmare whatsapp channel ko follow kr skte ho."
Important links :-
Algebraic Structure scope and importance
"Agar hm algebraic structure ke scope ki baat kre toh foundation of mathematics,Computer Science & IT , Cryptography, Engineering Applications, in sbhi jagah pr Algebraic structure ka use hota h which means algebraic structure future ke liye bohot important now talk about every point:
1. Mathematics foundation: Jitne bhi hmare Number system hote h jaise integers, rational, real etc ye sab group, ring, field in sb ke concept pr hi based hote h isiliye higher maths ko smjhne ke liye algebraic structure ko samjhna jruri h.
2. Computer Science and IT: Data structures , Automata Theory, Compiler design, Theory of computation in sbke andr hi Algebraic structure ka use hota h.
3. Cryptography and Cyber security: Algebraic Structure ka ek major scope cryptography mai bhi hota h. RSA, Diffle-Hellman, ECC in algorithm ko rings aur fields ke base pr hi bnaya jata h.
Notes of Algebraic Structure (Unit 4) DSTL
1. Algebraic Structure :- In simple language an Algebraic structure ek combination hota h ek non empty set aur uske upr perform hone wale operations ka. Operation jaise (+,x) lagate h aur wo operation fixed rules bhi follow krte h.
ex- If we have a non empty set A = {1,2,3} aur agar ab hm ispr addition (+) operation lagate h.
1+2 = 3
2+3 = 5
Toh ab ye ek Algebraic structure bn gya kyuki isme ek non empty set h aur operation define h.
#Components of an algebraic structure:-
1. Set :- Ek well define collection hota h unique elements ka.
2. Operation :- Operation jaise +,*,-
3. Properties:- Properties are following-
- Closure Property
- Associative Property
- Identity Property
- Inverse Property
#Types of Algebraic structure :--
Algebraic Structure following types ke hote h:
1. Semigroup - Jb hmare pass ek non empty set hota h aur uske sath uspr perform hone wala koi ek operation ho toh usko Semigroup khte h.
2. Monoid - Jb hmare pass koi semi group ho aur uske sath hi koi identity element ho toh usko Monoid khte h.
3. Group - Jb hmare pass koi monoid ho aur uske sath hi hmare pass inverse element bhi ho toh use ek Group khte h.
4. Ring - Jb hmare pass ek set ke sath do operation aa jae toh use Ring khte h.
5. Field - Jb hmare pass ek Ring ho aur uske sath wha division possible ho toh use Field khte h.
Weightage of Unit 4 (Algebraic Structure) in exam
"Agar hm Unit 4 Algebraic structure ke weightage ki baat kre toh exam ke andr hr unit ka weightage lagbhag same hota h lekin fir bhi ek baar aaiye iske weightage ko dekhte h. Unit 4 ka weightage Exam ke andr total 23-25 number ka hota h ye main exam jo semester wale hote h unka data h. Aur isse alag ye chapter real life bohot kaam ka h, kyuki iski application cyber security and cryptography mai h, agar kisi student ko cyber security ke field mai jana ho toh wo uske liye chapter bohot jaruri h."
Logic se Technology tk ka Connection
Discrete mathematics aur algebraic Structure sirf theory tak hi nai hote h balki inka direct use hota h technology ke andar. Logic se technology tak ka connection actually mathematical rules se shuru hota h, jo aage chal kar computer systems ke base banate h.
Sabse phle logic se shuruwat hoti h, Logic humein sikhata h ki koi statement true hai ya false. Ye concept computer ke liye bahut important hota h,kyuki computer sirf 0 and 1 ko samajhta h. jisme AND,OR,NOT jaise operations use hote h. ye operations algebric structure ke hi ek form hote h.
Unit 4 ka Conceptual Wrap-up
Unit 4 DSTL ka main focus concept ki clarity pr hota h. Is unit mai hmko ye pata chalta h ki Unit 4 ek rules and structure ka system na ki sirf mathematics aur sirf calculation ka. Algebraic structure ke through humein pata chalta hai ki set aur operation milkar kaise ek logical framework banate hain.
Is Unit ko padhane ke baad student ye identify kar pata hai ki kaunsa system simple hai aur kaunsa zyada powerful. Closure,identity aur inverse jaise concepts aage jaakar computer science ke advanced subjects jaise cryptography, automata theory aur programming logic ko samajhne mein madad karte hain.
Ye unit hme btati h ki hmko real life mai concept ko use krna kaise h kyuki bohot se student sirf conceptual knowledge gain kr lete h lekin mnn mai ye question rh jata h ki is conceptual knowledge ko hme use kha krna h isiliye ye unit hme btati h ki hmko hmari conceptual knowledge ko kha use krna h isiliye isko pdhna jaruri hai.
Now you have the notes and the strategy to score good marks, you can go and can prepare for the exams
If you want Unit 2 and unit 3 notes then click below 👇👇👇👇👇
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