Taking Notes

Here are a couple of tips for taking notes in the class.

Listen in Class.

Do not just write down what you see on the board. No teacher is going to write down every word they say and sometimes the important ideas won’t get written down.

Write Down Explanatory Remarks.

Make sure you write down any explanatory remarks the teacher makes. These often won’t get written down by the instructor, but can tell you how to work a particular kind of problem or why the instructor used one formula/method over another for a given problem.

Note Important Formulas/Concepts.

If teacher emphasizes a particular formula or concept then make note of it. This probably means it’s important and important formulas and concepts are much more likely to show up on an exam.

Question Your Teacher.

If you are unclear on something ask questions.

Note Topics You Don’t Understand.

If you are having trouble understanding something being presented note that in the margin and at least write down the key words. Leave yourself a couple of lines so you can fill in the missing details later once you’ve gotten help to understand the concept.

Review/Edit Your Notes.

As soon you can after class go back over your notes. Look for any errors and/or omissions. Fill in any information you didn’t have time to write down in class.

Review Regularly.

At regular intervals sit down and review your notes so that you can learn and retain the information. Remember, that this information will probably be required down the road so it’s best to learn it as soon as possible.

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History Of Maths (In Tamil)

கணிதம்


தென் அமெரிக்காவில் இருந்த பழம் மாயா மக்களின் எண்முறை
கணிதம் (Mathematics) என்பது வணிகத்தில், எண்களுக்கு இடையான தொடர்பை அறிவதில், நிலத்தை அளப்பதில், அண்டவியல் நிகழ்வுகளை வருவதுரைப்பதில் மனிதனுக்கு இருந்த கணித்தலின் தேவைகள் காரணமாக எழுந்த ஓர் அறிவியல் பிரிவாகும். இந்த நான்கு தேவைகளும் பின்வரும் நான்கு பெரிய கணிதப் பிரிவுகளை பிரதிபடுத்துகின்றன:
அளவு (quantity) - எண்கணிதம்
அமைப்பு (structure) - இயற்கணிதம்
வெளி (space) - வடிவவியல்
மாற்றம் (change) - பகுவியல் (analysis) - நுண்கணிதம்
ஆனால் இத்துடன் கணிதம் நிற்கவில்லை.

கணிதத்தில் பல்வகை நுட்பம் செறிந்த வடிவங்களைத் துல்லியமாக விளக்கலாம், அலசலாம். இப்படத்தைக் வரைபடமாகத் தரும் சார்பு:
பொருளடக்கம்
1 கணிதம் என்றால் என்ன?
2 தற்கால கணிதத்தின் விசுவரூபம்
3 கணிதக்கட்டுரை விமரிசனங்கள்
4 இந்தியக்கணித வரலாறு
5 தற்காலத்திய கணிதத்தின் வரலாறு
6 கணிதம் சம்பந்தமான பல்வேறு துணப் பிரிவுகள்
6.1 அளவு (Quantity)
6.2 அமைப்பு (Structure)
6.3 வெளி (Space)
6.4 மாற்றம் (Change)
6.5 கணித அடித்தளங்கள்
6.6 இலக்கமியல் கணிதம்
7 இவற்றையும் பார்க்கவும்



கணிதம் என்றால் என்ன?
எண்களை வைத்துக்கொண்டு உண்டாக்கப்பட்ட கணிப்பியலோ (arithmetic) வடிவங்களை வைத்துக்கொண்டு உண்டாக்கப்பட்ட வடிவியலோ இவைதான் கணிதவியல் என்று நினைப்போர் பலர். இன்னும் சிலர் எண்களுக்குப் பதிலாக குறிப்பீடுகளை வழங்கி அவைகளையும் எண்கள்போல் கணிப்புகள் செய்யும் இயற்கணிதம் தான் கணிதத்தின் முக்கிய பாகம் என்பர். மற்றும் சிலர் வடிவங்களை அலசி ஆராயும் வடிவியல் வளர்ச்சி தான் கணிதத்தின் இயல்பு என்று கூறுவர். ஆனால் கணிதம் இதையெல்லாம் தாண்டிய ஒன்று.

தற்கால கணிதத்தின் விசுவரூபம்

கணிதவியலின் இன்றைய வெளிப்பாடுகளில் இவையெல்லாம் ஒரு கடுகத்தனை பாகம் தான். கணிதம் எண்களில் தொடங்கியதும், எண்களிலும் வடிவங்களிலும் சிறந்த மேதாவிகள் புகுந்து விளையாடின ஈடுபாடுகளினால் பெரிய மரமாக வளர்ந்ததும் உண்மைதான். ஆனால் அத்துடன் அது நிற்கவே இல்லை. இன்று ஒரு அரிய தத்துவ இயலாக, வானளாவிய மரங்கள் கொண்ட பரந்த, செழித்த காடாகவே விசுவரூபம் எடுத்து இன்னும் வேகமாக வளர்ந்துகொண்டே இருக்கிறது. கணிதமில்லாமல் இன்று வேறு எந்தத் துறையுமே முன்னேற முடியாது என்று சொல்லும் அளவிற்கு, கணிதம் எல்லாத் துறைகளிலும் உள்ளார்ந்து படர்ந்திருக்கிறது.

கணிதக்கட்டுரை விமரிசனங்கள்

கணித விமரிசனங்கள் (Mathematical Reviews) என்ற ஒரு பத்திரிகை 1940 இல் ஒரு சில பக்கங்களுடன் தொடங்கி ஒவ்வொருமாதமும் கணிதத்தில் எழுதப்படும் புது ஆய்வுக்கட்டுரைகளை விமரிசிக்கவென்றே ஏற்படுத்தப்பட்டது. அது இன்று மாதத்திற்கு 2000 பக்கங்கள் கொண்டதாக வளர்ந்து, ஆயிரக்கணக்கான ஆய்வுப்பத்திரிகைகளிலிருந்து ஏறக்குறைய இருபது லட்சம் கட்டுரைகளின் விமரிசனத்தை கணிதப் பொக்கிஷமாகக் காத்து வருகிறது.

இந்தியக்கணித வரலாறு

"எண்ணென்ப ஏனை எழுத்தென்ப இவ்விரண்டும்
கண்ணென்ப வாழும் உயிர்க்கு" - திருவள்ளுவர்
என்று கூறி கணிதத்தின் முக்கியத்துவத்தை திருவள்ளுவர் 2000 வருடங்களுக்கு முன்பே நிலைநிறுத்தியுள்ளார். திருக்குறளில் ஒன்று, இரண்டு, மூன்று, நான்கு, ஐந்து, "அறு", "எழு", "எண்", பத்து, "கோடி" ஆகிய எண்கள் அல்லது தொகையீடுகள் அங்காங்கே பயன்படுத்தப்பட்டுள்ளன. எனினும் "தொண்டு" அல்லது "தொன்பது" பயன்படுத்தப்படவில்லை.

தமிழ் எண்ணுருக்கள், தமிழில் பூச்சியத்துக்கு குறியீடு இல்லை.
எண்களை எழுதுவதில் இடமதிப்புத் திட்டத்தையும் பூச்சியம் என்ற கருத்தையும் உருவாக்கி வருங்காலக்கணிதக்குறியீட்டுமுறைக்கு அடிகோலிட்டது பழையகால இந்தியா. இதைத்தவிர இந்தியக் கணிதவியலர்கள் (ஆரியபட்டர், பிரம்மகுப்தர், பாஸ்கராச்சாரியர், இன்னும் பலர்) மேற்கத்தியநாடுகள் மறுமலர்ச்சியடைந்து அறிவியலில் வளர்வதற்கு முன்னமேயே பலதுறைகளில் முன்னேற்றம் கண்டிருந்தனர்.
வேதகாலத்துக்கணிதத்தின் கணிப்பு முறைகள்
சுல்வசூத்திரங்களின் வடிவியல்

சூனியமும் இடமதிப்புத் திட்டமும்

எண்களின் அடிப்படைகளைப்பற்றி ஜைனர்கள்
பாக்சாலி கையெழுத்துப்பிரதிகளின் சமன்பாடுகள்
வானவியல்
கேரளத்தில் நுண்கணிதத்தின் முதல் கண்டுபிடிப்புகள்
இவையெல்லாம் இந்தியக்கணிதத்தின் சிறப்புகள்.

தற்காலத்திய கணிதத்தின் வரலாறு

14 வது நூற்றாண்டில் தொடங்கி, சென்ற ஆறு நூற்றாண்டுகளில் கணிதத்தின் வளர்ச்சியைத் தெரிந்துகொள்ள கணிதவியலாளர்கள் பலரின் வரலாறுகளே தக்க சான்றுகள். ஃபெர்மா, நியூட்டன், ஆய்லர், காஸ், கால்வா, ரீமான், கோஷி, ஏபல், வியர்ஸ்ட்ராஸ், கெய்லி, கேன்ட்டர், ஹில்பர்ட், இப்படி இன்னும் நூற்றுக்கணக்கானவர்கள் பங்கு கொண்டு உருவாக்கப்பட்ட கணிதம் இன்றைய கணிதம்.

கணிதம் சம்பந்தமான பல்வேறு துணப் பிரிவுகள்

கணிதத்தின் தற்காலப் பிரிவுகளைப் பற்றி பட்டியலிடவேண்டுமானால் அப்பட்டியலில் 100 தாய்ப்பிரிவுகளாவது இருக்கும். இப்பிரிவுகளுக்குள் மிகவும் வியப்பு தரும் உறவுகள் உண்டு. இவைகளிலெல்லாம் கணிதத்திற்கென்றே தனித்துவம் வாய்ந்த மரபும் குறிப்பிடத்தக்கது. இம்மரபுதான் கணிதத்தை மற்ற அறிவியல் துறைகளிலிருந்து பிரித்துக் காட்டுகிறது.இவைதவிர, கணிதத்தின் அடிப்படைகளுக்கும் மற்ற துறைகளுக்குமான தொடர்பை தருக்கவியலும் ஆய்கின்றது. மேலும் புள்ளியியல் போன்ற நேரடியாகப் பயன்படும் கணிதத் துறைகளும் உண்டு

அளவு (Quantity)
எண்கணிதம்
அளவியல்
இயல்பெண்கள்
முழு எண்கள்
விகிதமுறு எண்கள்
மெய்யெண்கள்
செறிவெண்கள்

அமைப்பு (Structure)
இயற்கணிதம்
எண் கோட்பாடு
நுண்புல இயற்கணிதம்
குலக் கோட்பாடு (Group Theory)
Order theory

வெளி (Space)
வடிவவியல்
முக்கோணவியல்
வகையீட்டு வடிவவியல் (Differential geometry)
இடவியல்
பகுவல்

மாற்றம் (Change)
நுண்கணிதம்
திசையன் நுண்கணிதம்
வகையீட்டு சமன்பாடுகள்
இயங்கியல் அமைப்புகள் (Dynamical systems)
ஒழுங்கின்மை கோட்பாடு

கணித அடித்தளங்கள்
தருக்கவியல் (கணிதம்)
கணக் கோட்பாடு, கணம் (கணிதம்)
விகுதிக் கோட்பாடு (Category theory)

இலக்கமியல் கணிதம்
சேர்வியல்
கணிமைக் கோட்பாடு
வரைவியல் (Cryptography)
கோலக்கோட்பாடு (Graph theory)

இவற்றையும் பார்க்கவும்
கணிதக் கலைச்சொற்கள் (ஆங்கில அகர வரிசையில்)
கணித மரபு
கணிதப் பிரிவுகளின் உறவுகள்
கணித அமைப்பு
கணிதத்தின் நிலைப்பிகள்

Source : Wikipedia

RESULT OF THE JOINT CSIR-UGC TEST FOR JUNIOR RESEARCH FELLOWSHIP (JRF) AND ELIGIBILITY FOR LECTURESHIP NET) HELD ON 22-06-2008

The candidates with following roll numbers have been declared successful in the category under which their roll numbers appear subject to the

condition of their fulfilling all the eligibility criteria for the test, viz. M.Sc. qualification with requisite percentage of marks, age etc.

 

1. Junior Research Fellowship(JRF-NET):The candidates whose roll numbers are listed below have qualified in the test for JRF-NET. These candidates are also eligible for Lectureship-NET.

 

(I) JRF(NET)CSIR:-

 

100010 100023 100039 100044 100055 100060 100073 100083 100172 100183 100193 100210 100248 100336 100366 100368 100375 100399 100400 100415

100433 100438 100461 100572 100889 100890 100895 100904 100912 100950 101015 101047 101066 101088 101171 101177 101215 101249 101270 101301

101325 101479 101480 101482 101508 101563 101565 101807 101823 101846 101853 101866 101869 101874 101916 101930 101966 102024 102112 102288

102303 102326 102356 102372 102379 102562 102591 102760 102765 102788 102916 103006 103158 103170 103273 103310 103361 103395 103432 103534

103541 103678 103703 103724 103835 103848 103961 104001 104126 104175 104181 104191 104221 104284 104286 104352 104444 104459 104475 104494

104495 104512 104525 104555 104580 104594 104668 104686 104734 104766 104800 104809 104818 104860 104863 104896 104923 104951 104962 104974

104979 104983 104990 105008 105024 105070 105083 105115 105125 105130 105166 105188 105222 105258 105277 105291 105316 105326 105418 105422

105467 105478 105483 105505 105511 105530 105539 105575 105604 105625 105638 105645 105653 105685 105708 105730 105855 105861 105867 105905

105946 105955 105960 105972 105974 105990 106008 106010 106024 106067 106101 106112 106144 106159 106172 106211 106236 106245 106249 106278

106284 106307 106318 106390 106400 106432 106436 106440 106456 106532 106535 106551 106563 106570 106571 106572 106581 106690 106701 106713

106718 106768 106797 106860 106872 106877 106905 106926 106929 106935 106963 107000 107034 107109 107118 107136 107149 107150 107185 107188

107263 107279 107281 107292 107301 107327 107342 107359 107395 107401 107423 107435 107451 107458 107474 107514 107523 107537 107566 107574

107596 107618 107636 107697 107705 107710 107744 107791 107812 107821 107828 107839 107848 107876 107891 107922 107932 107954 107974 108005

108015 108034 108086 108103 108109 108149 108179 108180 108185 108192 108237 108245 108257 108273 108304 108322 108372 108397 108398 108405

108407 108443 108444 108522 108537 108542 108586 108605 108617 108623 108635 108640 108662 108675 108678 108679 108683 108692 108734 108739

108742 108767 108773 108811 108816 108836 108846 108855 108858 108869 108909 108940 108955 108993 109007 109044 109058 109081 109120 109129

109136 109143 109146 109165 109168 109179 109249 109257 109263 109290 109312 109343 109351 109372 109387 109397 109406 109439 109481 109512

109515 109520 109536 109561 109563 109572 109573 109603 109610 109616 109618 109646 109650 109683 109691 109692 109693 109698 109719 109722

109732 109766 109807 109815 109840 109841 109855 109863 109885 110063 110080 110127 110130 110147 110176 110226 110241 110243 110265 110297

110320 110341 110344 110346 110365 110366 110378 110382 110416 110432 110441 110443 110444 110480 110492 110493 110517 110612 110625 110887

110917 110959 111011 111028 111070 111111 111120 111215 111222 111226 111240 111241 111248 111251 111254 111259 111260 111265 111282 111292

111293 111302 111317 111324 111351 111360 111365 111377 111386 111387 111393 111394 111416 111417 111423 111426 111428 111432 111440 111445

111448 111453 111468 111470 111476 111484 111485 111508 111522 111527 111532 111536 111539 111544 111550 111575 111577 111592 111597 111603

111622 111631 111638 111643 111656 111667 111690 111694 111702 111703 111735 111745 111746 111748 111750 111751 111752 111761 111765 111788

111808 111813 111816 111876 111881 111882 111893 111897 111909 111912 111925 111926 111931 111935 111938 111952 111957 111966 111977 111981

111987 111994 111997 112001 112030 112039 112042 112050 112060 112079 112080 112099 112107 112119 112122 112132 112137 112165 112172 112177

112181 112191 112193 112207 112215 112216 112218 112221 112222 112223 112257 112262 112263 112265 112267 112271 112278 112283 112290 112292

112310 112326 112330 112344 112346 112357 112358 112365 112375 112377 112379 112381 112385 112390 112398 112406 112409 112412 112415 112417

112418 112421 112427 112445 112453 112460 112469 112470 112471 112477 112479 112487 112490 112499 112518 112522 112534 112535 112537 112541

112548 112555 112569 112576 112579 112592 112596 112598 112602 112603 112612 112616 112620 112623 112807 112810 112941 113007 113011 113066

113091 113113 113114 113160 113193 113206 113283 113295 113320 113361 113364 113587 113607 113622 113651 113721 114126 114181 114188 114190

114192 114237 114252 114283 114320 114346 114379 114406 114457 114461 114464 114532 114534 114538 114555 114566 114590 114598 114650 114653

114669 114705 114720 114730 114735 114766 114816 114835 114902 114943 114992 115009 115015 115019 115059 115149 115171 115204 115254 115275

115323 115372 115527 115570 115600 115670 115672 115709 115721 115735 115770 115776 115813 115944 115998 116001 116107 116188 116223 116263

116347 116357 116396 116434 116472 116481 116518 116674 116699 116912 116929 116989 117017 117063 117154 117220 117226 117231 117236 117288

117325 117338 117352 117381 117433 117451 117457 117461 117481 117498 117500 117509 117515 117530 117534 117540 117547 117561 117563 117589

117590 117617 117641 117646 117687 117705 117737 117757 117760 117769 117891 117918 117948 117969 118006 118020 118055 118066 118088 118115

118167 118194 118236 118264 118329 118349 118363 118364 118434 118502 118750 118798 118819 118834 200167 200302 200346 200386 200515 200546

200568 200657 200715 200732 200736 200803 200817 200871 200873 200916 200936 200943 200952 200968 201019 201122 201206 201251 201264 201289

201291 201292 201316 300034 300047 300058 300059 300085 300146 300258 300359 300375 300527 300619 300715 300783 300828 300954 301216 301222

301243 301252 301286 301307 301374 301443 301494 301555 301567 301597 301654 301671 301734 302311 302410 302707 302795 302824 302851 303085

303181 303256 303266 303289 303366 303395 303420 303468 303538 303837 303902 303930 304051 304142 304216 304235 304534 304642 304778 304991

305011 305646 305799 305808 305810 305868 306015 306157 306259 306391 306468 306490 306540 306561 306597 306759 306802 306864 306949 307012

307049 307127 307145 307147 307176 307233 307465 307823 307884 307902 307923 307946 307952 308000 308010 308034 308049 308079 308082 308088

308096 308138 308140 308181 308202 308204 308211 308212 308218 308247 308280 308396 308406 308457 308462 308467 308478 308494 308565 308572

308596 308600 308603 308611 308617 308653 308675 308695 308718 308730 308736 308765 308781 308785 308797 308828 308837 308838 308842 308896

308901 308907 308933 308938 308944 308980 309013 309077 309081 309093 309203 309261 309292 309327 309338 309342 309343 309346 309349 309350

309373 309481 309489 309528 309537 309559 309566 309571 309576 309581 309594 309724 309736 309782 309787 309826 309845 309862 309864 309870

309942 309962 309966 309969 309974 309992 310012 310029 310044 310072 310094 310102 310154 310178 310196 310207 310243 310264 310273 310278

310282 310300 310319 310327 310338 310395 310436 310452 310491 310522 310608 310615 310632 310656 310665 310683 310723 310733 310741 310745

310759 310764 310804 310807 310855 310895 310911 310920 310921 310924 310925 310942 310977 310982 311003 311011 311013 311052 311078 311156

311183 311206 311216 311225 311296 311298 311299 311300 311355 311380 311406 311441 311463 311514 311558 311570 311577 311588 311595 311596

311616 311698 311710 311720 311785 311788 311796 311798 311803 311821 311832 311839 311876 311887 311896 311952 311969 311983 311986 312057

312139 312292 312374 312383 312519 312592 312674 312759 312865 312866 312870 312974 313044 313218 313243 313259 313296 313298 313494 313565

313587 313593 313651 313698 313740 313886 314180 314280 314300 314415 314457 314473 314715 314735 314736 314749 314978 315011 315012 315209

315235 315465 315555 315833 315979 316105 316140 316152 316333 316356 316367 316380 316394 316398 316432 316518 316593 316694 316759 316880

316912 316965 317040 317112 317128 317144 317210 317325 317399 317404 317415 317462 317467 317511 317528 317556 317594 317662 317685 317712

317718 317731 317749 317763 317788 317793 317815 317851 317900 317926 317936 317980 318014 318092 318149 318165 318255 318333 318364 318443

318454 318712 318739 318869 318884 318899 318931 318945 318965 319004 319018 319022 319045 319065 319085 319146 319148 319174 319180 319239

319251 319446 319513 319526 319633 319883 319886 320031 320096 320160 320230 320319 320359 320361 320363 320393 320400 320498 320541 320615

320654 320675 320680 320694 320793 320831 320858 320877 320901 320970 321007 321171 321444 321448 321535 321538 321758 321801 321835 321881

321945 321975 322000 322140 322331 322462 322471 322493 322514 322619 322623 322689 322761 322776 322790 322791 322831 322834 322835 322888

322897 322935 322975 323083 323099 323160 323173 323243 323249 323265 323365 323428 323439 323453 323458 323565 323574 323625 323629 323651

323706 323934 323952 324021 324138 324149 324212 324272 324465 324680 324843 324848 324872 324930 324944 325150 325212 325383 325538 325764

325786 326016 326069 326207 326231 326484 326488 326666 326740 326860 326874 326877 326974 327041 327150 327214 327278 327440 327490 327496

327745 327752 327792 327800 327828 327900 327907 327919 327932 327937 327977 328022 328073 328074 328108 328118 328217 328327 328330 328345

328354 328395 328423 328431 328445 328495 328573 328695 328725 328729 328779 328869 329006 400001 400145 400170 400174 400184 400216 400241

400469 400547 400777 400841 400892 401007 401078 401083 401100 401112 401127 401128 401359 401472 401475 401510 401561 401566 401681 401699

401719 401786 401929 401933 402031 402077 402605 402629 402845 402891 402935 402944 402955 402958 402961 402963 402972 402975 402980 402985

402995 403023 403054 403063 403068 403105 403117 403125 403180 403217 403260 403277 403292 403293 403335 403375 403409 403453 403465 403482

403551 403554 403560 403567 403605 403614 403616 403649 403676 403743 403747 403790 403894 403919 403920 403955 403967 403975 403976 404015

404262 404467 404651 404681 404784 404889 405020 405113 405208 405247 405344 405346 405403 405455 405534 405541 405543 405603 405612 405653

405704 405775 405793 405809 405886 405925 405929 405957 405958 405962 406046 406108 406149 406174 406176 406177 406212 406237 406318 406380

406417 406466 406613 406665 406670 406674 406830 407180 407224 407249 407260 407263 407311 407352 407385 407475 407548 407593 407645 407648

407756 407895 408133 408166 408172 408209 408537 408974 408980 408993 409045 409051 409118 409131 500004 500015 500018 500038 500125 500152

500166 500201 500231 500503 500596 500656 500659 500679 500817 500965 501047 501184 501208 501428 501451 501470 501486 501568 501571 501604

502373 502779 503035 503126 503218 503285 503295 503310 503323 503342 503365 503393 503403 503419 503436 503473 503479 503500 503533 503570

503628 503683 503716 503722 503762 503770 503772 503798 503801 503815 503819 503912 503946 503959 504002 504064 504081 504095 504112 504113

504170 504190 504191 504194 504222 504251 504282 504286 504299 504337 504414 504461 504575 504714 504716 504781 504988 505310 505462 505469

505482 505483 505535 505538 505782 505803 505807 505823 505980 505993 506091 506121 506158 506192 506249 506274 506317 506332 506362 506372

506469 506491 506527 506696 506733 506777 506804 506842 506872 506891 506894 506907 506951 506961 507031 507044 507050 507051 507057 507087

507088 507102 507142 507167 507232 507236 507263 507302 507361 507363 507454 507474 507584 507609 507641 507657 507719 507740 507746 508083

508114 508160 508213 508280 508312 508335 508356 508419 508448 508555 508652 508978 509068 509069 509125 509131 509173 509215 509533 510034

510250 510286 510316 510342 510390

 

(II) JRF(NET)UGC:-

 

100363 100480 101073 101149 101327 101441 101773 101893 101967 101979 102079 102144 102748 102868 102978 103035 103262 103398 104083 104102

104242 104329 104561 104675 104725 104757 104763 104811 104980 105252 105261 105283 105497 105716 105732 105827 105850 105851 105858 105937

105951 105963 105999 106082 106178 106324 106366 106473 106484 106584 106734 106859 106890 107023 107124 107385 107650 107719 107952 108134

108387 108587 108667 108890 108895 108949 109037 109056 109324 109358 109731 109813 109839 110160 110175 110237 110312 110401 110585 111023

111228 111280 111287 111325 111443 111531 111665 111730 111798 111858 111930 112006 112090 112106 112117 112136 112144 112174 112315 112325

112382 112788 112797 112927 113149 113261 113393 113653 113698 114133 114338 114354 114380 114401 114446 114529 114531 114533 114573 114591

115308 116017 116476 116500 116731 116927 117027 117053 117445 117753 117978 118304 118386 118467 118700 118776 200228 200872 200906 200947

201295 300241 301279 301554 302106 302874 303381 305155 307219 308279 308415 308518 308593 308805 308829 308903 309072 309104 309390 309545

309688 309759 310047 310172 310463 310684 310806 311033 311148 311332 311383 311511 311634 311855 311932 311958 311982 312607 312685 313289

313626 313748 313819 314032 314127 314498 314651 314969 315185 315293 316172 316210 316234 316256 316345 316580 316598 316813 316831 316876

317046 317142 317236 318184 318341 318579 318602 318630 318721 318914 319135 319188 319634 319817 320444 320506 320892 321189 321212 321738

321893 322001 322104 323833 324099 324264 324953 325115 325129 326455 326476 326560 326621 326869 326947 327477 328005 328144 328497 328930

400093 400558 400587 400896 400921 400955 400976 400996 402115 402348 402765 402843 403516 403629 403725 404031 404312 405118 405261 405901

406032 406204 406952 407227 407396 407818 407854 408108 408331 408474 500102 500860 501020 501585 501607 503174 503320 503608 503660 503900

504001 504480 504504 504532 504586 504984 505370 506477 506577 506715 506814 506973 507138 507416 508550 509063 509217 509236 510267 510325

 

2.Lectureship(NET):- The following candidates have qualified the eligibility test for Lectureship-NET. The candidates qualifying for Lectureship-NET will be eligible for recruitment as lecturer as well as for JRF-ship in a Scheme/Project, if otherwise suitable as per the eligibility criteria of that Scheme/Project. However, they will not be eligible for Regular JRF-NET Fellowship. They will be eligible to pursue Ph.D program with or without any fellowship other than JRF-NET.

 

100292 100320 100425 100612 100749 100853 100867 100883 100922 100931 100939 100981 101057 101058 101119 101126 101321 101393 101509 101521

101562 101711 101735 101746 101796 101834 101946 101978 102046 102188 102209 102289 102339 102342 102441 102557 102612 102643 102722 103093

103124 103154 103219 103278 103344 103408 103419 103463 103467 103472 103590 103723 103773 103784 103796 103818 103909 103957 104019 104051

104178 104182 104184 104185 104213 104217 104223 104248 104344 104345 104357 104364 104367 104375 104398 104447 104472 104499 104521 104528

104574 104581 104648 104665 104703 104759 104788 104806 104892 104893 104900 104948 104976 105026 105111 105112 105119 105121 105127 105179

105182 105259 105287 105318 105355 105419 105456 105461 105475 105537 105622 105672 105796 105889 105894 106065 106113 106161 106304 106326

106365 106372 106442 106488 106507 106568 106623 106636 106686 106756 106807 106845 106891 106975 107001 107075 107084 107104 107122 107159

107187 107315 107336 107430 107444 107471 107493 107552 107557 107563 107600 107641 107698 107730 107746 107756 107847 107898 107917 107937

107966 107972 107976 107997 108093 108110 108176 108178 108199 108334 108365 108416 108456 108465 108548 108556 108624 108718 108721 108737

108745 108870 108894 108971 108992 109078 109128 109133 109171 109198 109223 109231 109259 109319 109341 109345 109437 109450 109456 109484

109488 109575 109583 109585 109592 109627 109630 109641 109712 109749 109796 109834 109835 109854 109877 109912 109941 109943 109960 109962

110042 110055 110074 110092 110110 110163 110167 110168 110295 110353 110413 110417 110504 110736 110795 110828 110981 111037 111255 111330

111427 111461 111486 111487 111545 111564 111586 111627 111641 111653 111673 111715 111720 111722 111764 111789 111792 111805 111827 111866

111959 111962 111974 112009 112014 112066 112101 112129 112162 112163 112169 112232 112233 112240 112242 112284 112370 112372 112395 112402

112422 112456 112466 112468 112506 112531 112547 112565 112591 112677 112815 112826 112918 112928 113033 113051 113109 113115 113204 113209

113383 113439 113480 113598 113683 114030 114082 114085 114096 114104 114152 114155 114209 114240 114263 114265 114270 114293 114310 114314

114341 114364 114386 114440 114456 114458 114473 114488 114553 114567 114570 114664 114668 114676 114688 114689 114718 114722 115079 115124

115152 115214 115253 115331 115591 115683 115713 115738 115816 115885 116261 116510 116524 116526 116689 116710 116748 116808 116830 117058

117078 117125 117147 117165 117166 117170 117204 117207 117243 117275 117333 117373 117398 117430 117454 117478 117494 117512 117570 117581

117600 117647 117683 117697 117714 117850 117879 117881 118015 118029 118080 118084 118121 118126 118181 118202 118238 118274 118360 118442

118462 118571 118583 118585 118590 118632 118635 118655 118685 118699 118724 118756 118790 118792 118799 118800 118804 118880 118910 118921

118926 118934 201245 300046 300289 300364 300548 300549 300623 300691 300759 300918 301017 301244 301379 301487 301503 301505 301650 301651

301733 301778 302021 302148 302659 302883 303018 303058 303094 303105 303176 303186 303233 303248 303285 303353 303389 303412 303482 303483

303540 303754 303912 303950 304219 304263 304752 304892 304940 304942 305239 305345 306517 306698 306820 307141 307174 307396 307451 307517

307634 307725 307875 307905 307969 308129 308355 308362 308378 308387 308445 308485 308580 308583 308587 308601 308693 308714 308758 308779

308792 308964 308977 309084 309204 309535 309552 309591 309681 309711 309720 309807 309827 309869 309904 309930 310080 310242 310259 310304

310767 310790 310797 310817 310819 310832 310910 311056 311108 311121 311131 311140 311233 311248 311251 311368 311432 311500 311520 311547

311649 311756 311829 311860 311862 311874 311877 311955 312119 312434 312474 312586 312657 312731 312760 312824 312848 312872 312963 312967

313242 313244 313290 313410 313507 314272 314296 314441 314562 314585 314598 314723 314916 315134 315260 315261 315317 315434 316171 316205

316298 316362 316381 316567 316600 316618 316628 316659 316934 316983 317042 317229 317242 317267 317407 317603 317790 317803 317843 317853

317883 317941 317964 318072 318183 318257 318263 318298 318528 318570 318693 318708 319418 319666 319939 320060 320524 320532 320651 320689

320886 320952 321872 322037 322506 322555 322632 322886 322899 323013 323059 323069 323103 323147 323183 323203 323404 323429 323486 323656

323705 323763 323877 324047 324256 324951 324969 325044 325050 325060 325117 325370 325373 325413 325454 325458 325630 325632 325673 325751

325911 326150 326221 326478 326496 326600 326625 326756 326782 326812 326983 326994 327098 327122 327123 327366 327514 327520 327715 327785

327945 327954 328055 328381 328476 328582 328645 328686 328953 328967 328981 400233 400432 400485 400489 400530 400628 400638 400659 400669

400692 400812 400859 400869 401101 401115 401177 401220 401247 401298 401417 401463 401470 402000 402081 402098 402101 402155 402219 402446

402470 402624 402628 402634 402754 402773 402825 402842 403001 403008 403080 403084 403137 403164 403191 403341 403343 403396 403517 403538

403664 403705 404034 404097 404189 404226 404368 404383 404556 404679 404757 404825 404863 404881 405175 405234 405244 405260 405271 405337

405450 405581 405590 405659 405703 405734 405755 405805 405813 405853 405857 405861 405934 406188 406194 406253 406274 406305 406311 406338

406420 406938 407017 407297 407317 407470 407484 407544 407584 407687 407797 407929 408105 408268 408282 408362 408410 408479 408661 408883

408927 408970 408975 409072 409085 409104 500156 500325 500461 500573 500730 500916 500976 501010 501014 501107 501332 501511 501562 501698

501722 502040 502140 502271 502607 502610 502631 502717 502782 502889 503099 503223 503234 503249 503258 503259 503281 503336 503368 503395

503486 503532 503587 503728 503947 503978 504133 504153 504267 504363 504379 504401 504441 504468 504488 504540 504611 504612 504793 504995

505311 505338 505495 505788 505880 505983 505984 506039 506042 506060 506074 506125 506181 506271 506305 506466 506551 506594 506731 506815

506824 506923 506978 507003 507028 507043 507105 507110 507260 507266 507289 507312 507313 507437 507576 507629 507694 507824 508012 508097

508548 508696 508804 508941 508947 509128 509266 509347 509378 509621 509793 510035 510037 510062 510153 510169 510179 510187 510334

 

NOTE:- The council shall not be responsible for any printing error in the publication. No separate result intimation letters shall be issued. Successful candidates are required to send the attested copies of M.Sc. final year marksheet along with proof of date of birth and caste certificate if applicable.

Maths History-Notation

Notation, language, and rigor

Most of the mathematical notation in use today was not invented until the 16th century. Before that, mathematics
was written out in words, a painstaking process that limited mathematical
discovery.

In the 18th century, Euler was responsible for many of the notations in use today. Modern notation makes
mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict
syntax and encodes information that would be difficult to write in any other way.

Mathematical language can also be hard for beginners. Words such as or and only have more
precise meanings than in everyday speech. Additionally, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".

Rigor is fundamentally a matter of mathematical proof. Mathematicians want their
theorems to follow from axioms by means of systematic reasoning. This is to
avoid mistaken "theorems", based on fallible intuitions, of which many
instances have occurred in the history of the subject.The level of rigor
expected in mathematics has varied over time: the Greeks expected detailed
arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the
definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large
computations are hard to verify, such proofs may not be sufficiently rigorous. Axioms in traditional
thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of
an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a
firm axiomatic basis, but according to Gödel's incompleteness theorem every
(sufficiently powerful) axiomatic system has undecidable formulas; and so a
final axiomatization of mathematics is impossible.

Nonetheless mathematics is often imagined to be (as far as its formal content)
nothing but set theory in some axiomatization, in the sense that every mathematical
statement or proof could be cast into formulas within set theory.

Maths History - History

History

• The evolution of mathematics might be seen as an ever-increasing series of abstractions,
  or alternatively an expansion of subject matter.
• The first abstraction was probably that of numbers.
• The realization that two apples and two oranges have something in common was a
  breakthrough in human thought.
• In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time — days, seasons, years. Arithmetic
  (addition, subtraction,multiplication and division), naturally followed.
• Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.
• Numeralsystems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus. The Indus Valley civilization developed the modern decimal system, including the concept of zero.
• From the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations relating to taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics into the studies of quantity, structure,space, and change.
• since been greatly extended, and there has been a fruitful interaction between
  mathematics and science, to the benefit of both.
• Mathematical discoveries have been made throughout history and continue to be made today.
• According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American
  Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year.
• The overwhelming majorityof works in this ocean contain new mathematical theorems and
  their proofs."

Maths History - Etymology

• The word "mathematics" (Greek: μαθηματικά or mathēmatiká)
  comes from the Greek μάθημα (máthēma),
• which means learning, study, science, and additionally came to have the narrower and
• more technical meaning "mathematical study", even in Classical times.
• Its adjective is μαθηματικός (mathēmatikós), related to learning, or studious, which likewise further came to mean mathematical.
• In particular, μαθηματικὴτέχνη (mathēmatikḗ tékhnē), in Latin ars mathematica, meant the mathematical art.
• The apparent plural form in English, like the French plural form les mathématiques (and
  the less commonly used singular derivative la mathématique), goes back
  to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα
  μαθηματικά (ta mathēmatiká), used by Aristotle, and meaning roughly "all things
  mathematical".
• In English, however, the noun mathematics takes
  singular verb forms.
• It is often shortened to math in English-speaking
  North America and maths elsewhere.

Mathematics

• Mathematics is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them.
• Benjamin Peirce called it "the science that draws necessary conclusions".
• Other practitioners of mathematics maintain that mathematics is the science of pattern, and that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere.
• Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.
• Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life.
• Refinements of the basic ideas are visible in mathematical texts originating in the ancient Egyptian, Mesopotamian, Indian, Chinese, Greek and Islamic worlds.
• Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. The development continued in fitful bursts until the Renaissance period of the 16th century, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.
  
• Today, mathematics is used throughout the world in many fields, including natural science, engineering, medicine, and the social sciences such as economics. Applied mathematics, the application of mathematics to such fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines.
• Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although applications for what began as pure mathematics are often discovered later.

SET EXAM- Mathematics Paper III

Mathematics Paper III (Unit 16 to 24)

16. Linear Integral Equations :
Linear integral Equations of the first and second kind of Fredholm and Volterra type, solution by successive substitutions and successive approximations ; Solution of equations with separable kernels ; The Fredholm Alternative ; Holbert – Schmidt theory for symmetric kernels.
17. Numerical analysis :
Finite differences, interpolation ; Numerical solution of algebric equation ; Iteration ; Newton – Rephson method ; Solution on linear system ; Direct method ; Gauss elimination method ; Matrix – Inversion, elgenvalue problems ; Numerical differentiation and integration.Numerical solution of ordinary differential equation; iteration method, Picard’s method, Euler’s method and improved Euler’s method.
18. Integral Transform :
Laplace transform ; Transform of elementary functions, Transform of Derivatives, inverse Transform, Comrolution Theorem, Applications, Ordinary and Partial differential equations ; Fourier transforms ; sine and cosine transform, Inverse Fourier Transform, Application to ordinary and partial differential equations. 19. Mathematical Programming :
Revised simplex method, Dual simplex method, Sensitivity analysis and parametric linear programming. Kuhn – Tucker conditions of optimality. Quadratic programming ; methods due to Beale, Wofle and Vandepanne, Duality in quadranic programming, self duality, integer programming.
20. Measure Theory :
Measurable and measure spaces ; Extension of measures, signed measures, Jordan – Hahn decomposition theorems. Integration, monotone convergence theorem, Fatou’s lemma, dominated convergence theorem. Absolute continuity. Radon Nikodym theorem, Product measures, Fubini’s theorem.
21. Probability :
Sequences of events and random variables ; Zero – one laws of Borel and Kolmogorov. Almost sure convergence, convergence in mean square, Khintchine’s weak law of large numbers ; Kolmogorov’s inequality, strong law of large numbers.Convergence of series of random variables, three – series criterion. Central limit theorems of Liapounov and Lindeberg – Feller. Conditional expectation, martingales.
22. Distribution Theory :
Properties of distribution functions and characteristic functions ; continuity theorem, inversion formula, Representation of distribution function as a mixture of discrete and continuous distribution functions ; Convolutions, marginal and conditional distributions of bivariate discrete and continuous distributions.Relations between characteristic functions and moments ; Moment inequalities of Holder and Minkowski.
23. Statistical Inference and Decision Theory :
Statistical decision problem : non – randomized, mixed and randomized decision rules ; risk function, admissibility, Bayes’ rules, minimax rules, least favourable distributions, complete class, and minimal complete class. Decision problem for finite parameter class. Convex loss function. Role of sufficiency.Admissible, Bayes and minimax estimators ; Illustrations, Unbiasedness. UMVU estimators. Families of distributions with monotone likelihood property, exponential family of distributions. Test of a simple hypothesis against a simple alternative from decision – theoretic view point. Tests with Neymen structure. Uniformly most powerful unbiased tests. Locally most powerful tests. Inference on location and scale parameters estimation and tests. Equivariant estimators invariance in hypothesis testing.
24. Large sample statistical methods :
Various modes of convergence, Op and op, CLT Sheffe’s theorem, Polya’s theorem and Stutsky’s theorem. Transformation and variance stabilizing formula. Asymptotic distribution of function of sample moments. Sample quantities. Order statistics and their functions. Tests on correlations, coefficients of variation, skewness and kurtosis. Pearson Chi-square, contingency. Chi – square and likelihood ratio statistics. U – statistics. Consistency of Tests. Asymptotic relative efficiency.



Mathematics Paper III  (Unit 31 to 34)

31. Demography and Vital Statistics :
Measures of fertility and mortality, period and Cohort measures.Life tables and its applications ; Methods of construction of abridged life tables. Application of stable population theory to estimate vital rates. Population projections, Stochastic models of fertility and reproduction.
32. Industrial Statistics :
Control charts for variables and attributes ; Acceptance sampling by attributes ; single, double and sequential sampling plans ; OC and ASN functions, AOQL and ATI ; Acceptance sampling by varieties. Tolerance limits. Reliability analysis : Hazard function, distribution with DFR and IFR ; Series and parallel systems. Life testing experiments.
33. Inventory and Queueing theory :
Inventory ( S, S ) policy, periodic review models with stochastic demand. Dynamic inventory models. Probabilistic re-order point, lot size inventory system with and without lead time. Distribution free analysis. Solution of inventory problem with unknown density function. Warehousing problem. Queues ; Imbedded Markov Chain method to obtain steady state solution of M/G/1, G/M/1 AND M/D/C, Network models. Machine maintenance models. Design and control of queueing systems.
34. Dynamic Programming and Marketing :
Nature of dynamic programming, Deterministic processes, Non-sequential discrete optimization – allocation problems, assortment problems. Sequential discrete optimization long – term planning problems, multi stage production processes. Functional approximations. Marketing systems, application of dynamic programming to marketing problems. Introduction of new product, objective in setting market price and its policies, purchasing under fluctuating prices, Advertising and promotional decisions, Brands switching analysis, Distribution decisions.

Mathematics Paper III (Unit 1 to 6)

1. Real Analysis :
Riemann integrate functions ; improper integrate, their convergence and uniform convergence. Eulidean space R¯ , Boizano – Weleratrass theorem, compact. Subsets of R•, Heine – Borel theorem, Fourier series.Continuity of functions on R”, Differentiability of F : R• > Rm, Properties of differential, partial and directional derivatives, continuously differentiable functions. Taylor’s series. Inverse function theorem, implicit function theorem.Integral functions, line and surface integrals, Green’s theorem. Stoke’s theorem.
2. Complex Analysis :
Cauchy’s theorem for convex regions, Power series representation of Analytic functions. Liouville’s theorem, Fundamental theorem of algebra, Riemann’s theorem on removable singularities, maximum modulus principle. Schwarz lemma, Open Mapping theorem, Casoratti – Weierstrass – theorem, Weierstrass’s theorem on uniform convergence on compact sets, Bilinear transformations, Multivalued Analytic Functions, Riemann Surfaces.
3. Algebra :
Symmetric groups, alternating groups, Simple groups, Rings, Maximal ideals, Prime ideals, integral domains, Euclidean domains, principal ideal domains, Unique Factorisation domains, quotient fields, Finite fields, Algebra of Linear Transformations, Reduction of matrices to Canonical Forms, Inner Product Spaces, Orthogonality, quadratic Forms, Reduction of quadratic forms.
4. Advanced Analysis :
Elements of Metric Spaces, Convergence, continuity, compactness, Connectedness, Weierstrass’s approximation Theorem. Completeness, Bare category theorem, Labesgue measure, Labesgue integral, Differentiation and integration.
5. Advanced Algebra :
Conjugate elements and class equations of finite groups, Sylow theorems, solvable groups, Jordan Holder Theorem, Direct Products, Structure Theorem for finite abelian groups, Chain conditions on Rings : Characteristic of Field, Field extensions, Elements of Galois theory, solvability by Radicals, Ruler and compass construction.
6. Functional Analysis :
Banach Spaces, Hahn – Banach Theorem, Open mapping and closed Graph Theorems. Principle of Uniform boundedness, Boundedness and continuity of Linear Transformations. Dual Space, Embedding in the second dual, Hilbert Spaces, Projections. Orthonormal Basis, Riesz – representation theorem. Bessel’s inequality, parsaval’s identity, self adjoined operators, Normal Operators.

Mathematics Paper III (Unit 25 - 30)

25. Multivariate Statistical Analysis :
Singular and non – singular multivariate distributions. Characteristics functions. Multivariate normal distribution ; marginal and conditional distribution, distribution of linear forms, and quadratic forms, Cochran’s theorem.
Inference on parameters of multivariate normal distributions : one – population and two – population cases. Wishart distribution. Hotellings T2, Mahalanobis D2, Discrimination analysis, Principal components, Canonical correlations, Cluster analysis.
26. Linear Models and Regression :
Standard Gauss – Markov models ; Estimability of parameters ; best linear unbiased estimates ( BLUE ); Method of least squares and Gauss – Markov theorem ; Variance – covariance matrix of BLUES.
Tests of linear hypothesis ; One – way and two – way classifications. Fixed, random and mixed effects models ( two – way classifications only ); variance components, Bivariate and multiple linear regression; Polynomial regression ; use of orthogonal polynomials. Analysis of covariance. Linear and nonlinear regression. Outliers.
27. Sample Surveys : Sampling with varying probability of selection, Hurwitz – Thompson estimator ; PPS sampling ; Double sampling, Cluster sampling. Non-sampling errors ; interpenetrating samples. Multiphase sampling. Ratio and regression methods of estimation.
28. Design of Experiments :
Factorial experiments, confounding and fractional replication. Split and strip plot designs ; Quesi – Latin square designs ; Youden square. Design for study of response surfaces ; first and second order designs. Incomplete block designs ; Balanced, connectedness and orthogonality, BIBD with recovery of inter-block information, PBIBD with 2 associate classes. Analysis of sense of experiments, estimation of residual effects. Construction of orthogonal – Latin squares, BIB designs, and confounded factorial designs. Optimality criteria for experimental designs.
29. Time – Series Analysis :
Discrete – parameter stochastic processes ; strong and weak stationarity ; autocovariance and autocorrelation, Moving average, autoregressive, autoregressive moving average and autoregressive integrated moving average processes. Box – Jenkins models. Estimation of the parameters in ARIMA models, forecasting. Perfodogram analysis.
30. Stochastic Processes :
Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution ; branching processes ; Random walk ; Gambler’s ruin. Markov processes in continuous time ; Poisson processes, birth and death processes, Wiener process.

SET EXAM Mathematics Paper II

1. Basic concepts of Real and Complex analysis :

Sequences and series, continuity, uniform continuity, Differentiability, Mean Value Theorem, sequences and series of functions, uniform convergence, Riemann integral – definition and simple properties. Algebra of Complex numbers, Analytic functions. Cauchy’s Theorem and integral formula, Power series, Taylor’s and Laurent’s series, Residues, Contour integration.


2.Basic Concepts of Linear Algebra :

Space of n-vectors, Linear dependence, Basis, Linear transformation, Algebra of matrices, Rank of a matrix, Determinants, Linear equations, Quadratic forms, Characteristic roots and vectors.

3.Basic concepts of probability :

Sample space, discrete probability, simple theorems on probability, independence of events, Bayes Theorem. Discrete and continuous random variables, Binomial, Paisson and Normal distributions ; Expectation and moments, independence of random variables, Chebyshev’s inequality.

4. Linear Programming Basic Concepts:

Convex sets. Linear Programming Problem ( LPP ). Examples of LPP, Hyperplane, open and closed half – spaces. Feasible, basic feasible and optimal solutions. Extreme point and graphical method.

5. Real Analysis :

Finite, countable and uncountable sets, Bounded and unbounded sets. Archimedean property, ordered field, completeness of R, Extended real number system, liens up and limits of a sequence, the epsilon – delta definition of continuity and convergence, the algebra of continuous functions, monotonic functions, types of discontinuities, infinite limits and limits at infinity, functions of bounded variation, elements of metric spaces.

6.Complex Analysis:

Riemann Sphere and Stereographic projection. Lines, Circles, crossratio. Mobius transformations, Analytic functions, Cauchy - Riemann equations, line integrals, Cauchy's theorem, Morera's theorem, Liouville's theorem, integral formula, zero-sets of analytic functions, exponential, sine and cosine functions, Power series representation, Classification of singularities, Conformal Mapping.


7. Algebra:

Group, subgroups, Normal subgroups, Quotient Groups, Homomorphisms, Cyclic Groups, permutation Groups, Cayley's Theorem, Rings, Ideals, Integral Domains, Fields, Polynomial Rings.


8.Linear Algebra:

Vector spaces, subspaces, quotient spaces, Linear independence, Bases, Dimension. The algebra of linear Transformations, kernel, range, isomorphism, Matrix Representation of a linear transformation, change of bases, Linear functionals, dual space, projection, determinant function, eigenvalues and eigen vectors, Cayley-Hamilton Theorem, Invariant Sub-spaces, Canonical Forms: diagonal form, Triangular form, Jordan Form, Inner product spaces.


9. Differential Equations:

First order ODE, singular solutions, initial value Problems of First Order ODE, General theory of homogeneous and non-homogeneous Linear ODE, Variation of Parameters. Lagrange's and Charpit's methods of solving first order Partial Differential Equations. PDE's of higher order with constant coefficients.


10.Data Analysis Basic Concepts:

Graphical representation, measures of central tendency and dispersion. Bivariate data, correlation and regression. Least squares - polynomial regression, Applications of normal distribution.


11.Probability: Axiomatic definition of probability. Random variables and distribution functions (univariate and multivariate); expectation and moments; independent events and independent random variables; Bayes' theorem; marginal and conditional distribution in the multivariate case, covariance matrix and correlation coefficients (product moment, partial and multiple), regression.
Moment generating functions, characteristic functions; probability inequalities (Tchebyshef, Markov, Jensen). Convergence in probability and in distribution; weak law of large numbers and central limit theorem for independent identically distributed random variables with finite variance.
12.Probability Distribution: Bernoulli, Binomial, Multinomial, Hypergeomatric, Poisson, Geometric and Negative binomial distributions, Uniform, exponential, Cauchy, Beta, Gamma, and normal (univariate and multivariate) distributions Transformations of random variables; sampling distributions. t, F and chi-square distributions as sampling distributions, Standard errors and large sample distributions. Distribution of order statistics and range.
13. Theory of Statistics: Methods of estimation: maximum likelihood method, method of moments, minimum chi-square method, least-squares method. Unbiasedness, efficiency, consistency. Cramer-Rao inequality. Sufficient Statistics. Rao-Blackwell Theorem. Uniformly minimum variance unbiased estimators. Estimation by confidence intervals. Tests of hypotheses: Simple and composite hypotheses, two types of errors, critical region, randomized test, power function, most powerful and uniformly most powerful tests. Likelihood-ratio tests. Wald's sequential probability ratio test.
14. Statistical methods and Data Analysis: Tests for mean and variance in the normal distribution: one-population and two- population cases; related confidence intervals. Tests for product moment, partial and multiple correlation coefficients; comparison of k linear regressions. Fitting polynomial regression; related test. Analysis of discrete data: chi-square test of goodness of fit, contingency tables. Analysis of variance: one-way and two-way classification (equal number of observations per cell). Large-sample tests through normal approximation. Nonparametric tests: sign test, median test, Mann-Whitney test, Wilcoxon test for one and two-samples, rank correlation and test of independence.
15. Operational Research Modelling: Definition and scope of Operational Research. Different types of models. Replacement models and sequencing theory, Inventory problems and their analytical structure. Simple deterministic and stochastic models of inventory control. Basic characteristics of queueing system, different performance measures. Steady state solution of Markovian queueing models: M/M/1, M/M/1 with limited waiting space M/M/C, M/M/C with limited waiting space.
16.Linear Programming: Linear Programming, Simplex method, Duality in linear programming. Transformation and assignment problems. Two person-zero sum games. Equivalence of rectangular game and linear programming.
17. Finite Population: Sampling Techniques and Estimation: Simple random sampling with and without replacement. Stratified sampling; allocation problem; systematic sampling. Two stage sampling. Related estimation problems in the above cases.
18. Design of Experiments: Basic principles of experimental design. Randomisation structure and analysis of completely randomised, randomised blocks and Latin-square designs. Factorial experiments. Analysis of 2n factorial experiments in randomised blocks.

SET EXAM - Mathematics Paper III (Unit 7-15)

7. Topology:
Elements of Topological Spaces, Continuity, Convergence, Homeomorphism, Compactness, Connectedness, Separation Axioms, First and Second Countability, Separability, Subspaces, Product Spaces, quotient spaces. Tychonoff's Theorem, Urysohn's Metrization theorem, Homotopy and Fundamental Group.
8.Discrete Mathematics:
Partially ordered sets, Lattices, Complete Lattices, Distributive lattices, Complements, Boolean Algebra, Boolean Expressions, Application to switching circuits, Elements of Graph Theory, Eulerian and Hamiltonian graphs, planar Graphs, Directed Graphs, Trees, Permutations and Combinations, Pigeonhole principle, principle of Inclusion and Exclusion, Derangements.
9.Ordinary and Partial Differential Equations:
Existence and Uniqueness of solution dy/dx =f(x,y) Green's function, sturm Liouville Boundary Value Problems, Cauchy Problems and Characteristics, Classification of Second Order PDE, Separation of Variables for heat equation, wave equation and Laplace equation, Special functions.
10.Number Theory:
Divisibility; Linear diophantine equations. Congruences. Quadratic residues; Sums of two squares, Arithmetic functions Mu, Tau, Phi and Sigma ( and ).
11.Mechanics:
Generalised coordinates; Lagranges equation; Hamilton's cononical equations; Variational principles - Hamilton's principles and principles of least action; Two dimensional motion of rigid bodies; Euler's dynamical equations for the motion of rigid body; Motion of a rigid body about an axis; Motion about revolving axes.
12.Elasticity:
Analysis of strain and stress, strain and stress tensors; Geometrical representation; Compatibility conditions; Strain energy function; Constitutive relations; Elastic solids Hookes law; Saint-Venant's principle, Equations of equilibrium; Plane problems - Airy's stress function, vibrations of elastic, cylindrical and spherical media.
13.Fluid Mechanics:
Equation of continuity in fluid motion; Euler's equations of motion for perfect fluids; Two dimensional motion complex potential; Motion of sphere in perfect liquid and motion of liquid past a sphere; vorticity; Navier-Stokes's equations for viscous flows-some exact solutions.
14.Differetial Geometry:
Space curves - their curvature and torsion; Serret Frehat Formula; Fundamental theorem of space curves; Curves on surfaces; First and second fundamental form; Gaussian curvatures; Principal directions and principal curvatures; Goedesics, Fundamental equations of surface theory.
15.Calculus of Variations:
Linear functionals, minimal functional theorem, general variation of a functional, Euler- Lagrange equation; Variational methods of boundary value problems in ordinary and partial differential equations.

List of Indian mathematicians

• The chronology of Indian mathematics spans from the Indus valley civilization and the Vedas to Modern times.
• Indian mathematicians have made a number of significant contributions to mathematics including place-value arithmetical notation and the concept of zero.
  
  Vedic
  the Shatapatha Brahmana contains calculations related to altar construction.
  Panini, ca. 5th c. BC, Algebraic grammarian
  
  
  Classical
• Post-Vedic Sanskrit to Pala period mathematicians (5th c. BC to 11th c. AD)
• Aryabhata - Astronomer who gave accurate calculations for astronomical constants, 476-520
• Brahmagupta - Helped bring the concept of zero into arithmetic
• Matanga Muni - Combinatorics in music
• Shridhara (between 650-850) - Gave a good rule for finding the volume of a sphere.
  
  
  Medieval to Mughal period
  
  13th century to 1800.

• Gangesha Upadhyaya, 13th century, Logician, mithila school
• Pakshadhara, son of Gangehsa, Logician, Mithila school
• Shankara Mishra, Logician, Mithila school
• Narayana Pandit
• Madhava - Discovered some elements of Calculus
• Parameshvara (1360-1455), discovered drk-ganita, a mathematical model of astronomy based on observations, Madhava's Kerala school
• Nilakantha Somayaji,1444-1545 - Mathematician and Astronomer, Madhava's Kerala school
• Mahendra Suri (14th century)
• Shankara Variyar (c. 1530)
• Vasudeva Sarvabhauma, 1450-1525, Logician, Navadvipa school
• Raghunatha Shiromani, (1475-1550), Logician, Navadvipa school
• Jyeshtadeva , 1500-1610, Author of Yuktibhasa, Madhava's Kerala school
• Achyuta Pisharati, 1550-1621, Astronomer/mathematician, Madhava's Kerala school
• Mathuranatha Tarkavagisha, c. 1575, Logician, Navadvipa school
• Jagadisha Tarkalankara, c. 1625, Logician, Navadvipa school
• Gadadhara Bhattacharya, c. 1650, Logician, Navadvipa school
• Munishvara (17th century)
• Kamalakara (1657)
• Jagannatha Samrat (1730)
  
  
  Born in 1800s
• 
  Srinivasa Ramanujan (1887-1920)
• A. A. Krishnaswami Ayyangar (1892-1953)
• Prasanta Chandra Mahalanobis (1893-1972)
• Satyendra Nath Bose (1894-1974)
• Sanjeev Shah (1803- 1896)
• Raghunath Purushottam Paranjape
  
  
  Born in 1900s

• Vijay Manohar (1901-1987)
• S. N. Roy (1906-1966)
• Sarvadaman Chowla (1907-1995)
• Subrahmanyan Chandrasekhar (1910-1995)
• D.K. Ray-Chaudhuri
• Harish-Chandra (1920-1983)
• C. R. Rao (1920-)
• Shreeram Shankar Abhyankar (1930-)
• Ramdas Lotu Bhirud(1937-1997)
• Jayant Narlikar (1930-)
• Vijay Kumar Patodi (1945-1976)
• Narendra Karmarkar (1957-)
• M.V. Subbarao (1921-2006)
• Navin M. Singhi
• S. S. Shrikhande
• Raj Chandra Bose
• Parthasarathy, K. R.
• Ramenjit Singh
• Gaurav Agrawal
  
  
  
  

General Tips for Studying Mathematics

Go To Class Regularly:

Remember that math is cumulative. If you don’t go to class you will miss important material that will be used in later sections and important announcements.

Get to Class On Time.

Sometime important announcements are only given during the first few minutes of a class.

LISTEN During Class.

In order to get something out of the class you need to listen while in class. Often this can be difficult to do but it is very important. Sometimes important ideas will not be written down on the board, but instead just spoken by the teacher.  

Watch for things the teacher emphasizes, even if just in words. This often means the teacher thinks it’s important. The more important that  teacher thinks a topic is, the more likely that it will show up on the exam!

Take Good Notes.

Try to write down everything that teacher puts on board. It may seem easy when watching the teacher, but it often is not so easy when it comes time for you to do it. A good set of notes will help remind you how to do these problems. For some teacher writing down everything may be difficult. In these cases you should try to write down as much as possible.

Note as well that this seems to contradict the previous tip. It is often hard to both listen and take a good set of notes. This is something that one often only gains with practice. You need to be able to listen while you are writing down the important parts of the lecture.  

Ask Questions.

If you don’t understand something then ask your teacher. Chances are you are not the only one who doesn’t understand.

Listen When Others Ask Questions.

When other students ask questions make sure you listen to both the question and the answer. It may be that the student asking the question thought of something that you didn’t think of.

Review Notes After Class.

After each class you should review your notes. Note the topics that you found confusing and formulate questions that you can ask your teacher or tutor to help you understand the topic.

Make a Set of Index Cards.

Make a set of index cards with important formulas and concepts on them. You can carry these around with you to look over when you’ve got a few spare minutes. Use them to help you memorize the important formulas and concepts.

Note Due Dates. Write down the due dates for homework and dates for exams someplace you’ll see them so you don’t forget about them.
Budget Adequate Time For Studying/Homework. It often takes more time studying mathematics to learn the subject than you may require in other classes.  

Do Homework After Each Class.

At the end of each class budget some time to look over the homework from that days lecture and attempt to do it Doing this will allow you time to really work at understanding the concepts covered that day. Do not wait until the last minute to do the homework as this often results in an incomplete homework set and an incomplete understanding of the concept.  

Do Homework Without Notes and Book.

After the first few homework problems, put your notes and book up and try to do the remaining problems without referring to your notes and/or book. In most cases you will not have these during your exams so get used to doing problems without them.

Do More Homework.

Do not limit yourself to just the homework that your instructor assigns. The more problems that you work the better off you’ll be.

Practice, Practice, Practice.

Practice as much as possible. The only way to really learn how to do problems is work lots of them. The more you work, the better prepared you will be come exam time.

Persevere.

You will not just instantly get every topic that is covered in a math class. There will be some topics that you will have to work at before you completely understand. The only way to really grasp some topics is to go home and think about it and work some problems. You will often find that after a little work a topic that initially baffled you will all of a sudden make sense.

Keep Old Homework and Exams.

Do not throw away homework and exams once you get them back. The homework is a good source of study material for exams and both the homework and exams is a good source of study material for comprehensive final exams (if you’ve got one).

Don’t Forget Your Textbook.

If you get stuck on a topic that was discussed in class do not forget that you do have a textbook. Often the text book will contain examples not worked in class and/or a different approach to a problem.

Seek Help If You Need It.

If you are having trouble with your maths class you have many options open to you and you should take advantage of them. You can go to your tescher’s office hours, go to the tutoring room or hire a tutor to get help. 

X-MATRIC MATHS Blue Print

S.No.	Chapter Name	Marks
1.	Number Work	25
2.	Mensuration	24
3.	Set Language	21
4.	Consumer Arithmetic	17
5.	Algebra	33
6.	Graphs	20
> >	Total Marks	140

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> >

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       MATHEMATICS - II

S.No.	Chapter Name	Marks
1.	Matrices	17
2.	Theoretical Geometry	26
3.	Co-ordinate Geometry	33
4.	Trigonometry	28
5.	Statistics	16
6.	Practical Geometry	20
> >	Total Marks	140

> >