4year1

Four Year Undergraduate

Course Structure

DEPARTMENT OF MATHEMATICS

Four Year Undergraduate Programme

with Multiple Degree Option

Semester FC DC-I DC-II AC IMBH/CA

1 4 2 1-IMBH

2 3 2 1* 1-IMBH

3 2 2 1 1 1-CA

4 2 2 1 1 1-CA

5 3 1 1 1-CA5 3 1 1 1-CA

6 3 1 1 1-CA

7 2+1(Res Meth) 1 1-CA

8 2+1(Res) 1 1-CA

FC Foundation Course DC-I Discipline Course – I

DC-II Discipline Course – II AC Applied Courses

IMBH Integrating Mind, Body & Heart

CA Cultural Activities include NCC, Sports, NSS, etc.

* Language Course

Foundation Courses

• Language, Literature, and Creativity –I (Hindi/MIL)

• Language, Literature, and Creativity –II (English)

• Information Technology

• Business, Entrepreneurship, and Management

• Governance and Citizenship

• Psychology, Communication and Life Skills• Psychology, Communication and Life Skills

• Geographic and Socio-Economic Diversity

• Science and Life

• History, Culture and Civilization

• Building Mathematical Ability

• Environment and Public Health

Teaching Hours• Foundation Course: Language, Literature, and

Creativity to be offered in semester 1st and semester

2nd : 5 periods/week (4 lectures + 1 student’s

presentation) Hindi/Sanskrit/MIL/Persian/Arabic/

English

• Others foundation papers: 3 periods/week (2 lectures

+ 1 student’s presentation)+ 1 student’s presentation)

• DC-I & DC-II : 5 periods/week(4 lectures + 1 student’s

presentation)

• Applied Course: 3 periods/week(2 lectures + 1

student’s presentation)

• IMBH/CA: 2periods/week (to be part of the

workload)

• Tutorial/Practical will continue wherever applicable

Degree Nomenclature

• Associate Baccalaureate after 2 years

• Baccalaureate after 3 years

• Baccalaureate with Honours/B Tech. after 4

yearsyears

Semester No/ of Papers Papers

1 2Calculus-I (Practical)

Algebra-I

2 2Analysis-I

Differential Equations-I (Practical)

3 2Calculus-II

Numerical Methods (Practical)

4 2Analysis-II

Probability & Statistics (Practical)

Tentative Structure of DC-I

5 3

Algebra-II

Analysis-III

Diff. Eqns.-II (Practical)

6 3

Algebra-III

Analysis-IV

Calculus of Variations & Optimization

(Practical)

7 2+1Algebra-IV

Differential Equations-III (Practical)

8 2+1Analysis-V (Practical)

Number Theory


1

2

3 1 MAPT-101 Calculus & Matrices

4 1 MAPT-202 Calculus & Geometry

Tentative Structure of DC-II

4 1 MAPT-202 Calculus & Geometry

5 1 MAPT-303 Algebra

6 1 MAPT-404 Differential Equations

7 1 MAPT-505 Real Analysis

8 1 MAPT-606 Discrete Mathematics


1

2

3 1 Mathematical Biology

4 1 Mathematical Finance

Tentative Structure of Applied Courses

5 1Cryptography and Network

Systems

6 1 Applications of Algebra

7

8

1. ARSD B.K. Tyagi 9911469696

2. DDU Sanjay Pant 9810528236

3. Dayal Singh Arun Pal Singh 9582588065

4. Hans Raj Jyoti Bhola 9953681378

5. IP Col W Sarita Anand 9873764067

Calculus (2) and Analysis (5) papersConveners : Sachi Srivastava (7838266611)

Shashi Kiran (9910112456)

5. IP Col W Sarita Anand 9873764067

6. JMC Alka Marwaha 9891361608

7. Keshav Hemant Kumar Singh 9312340064

8. Kirori Mal Pawan Bala 9868436022

9. Kamal Nehru Kanta Gupta 9810967543

10. LSR Uma Varsha Kakkar 9868177371

11. Maitreyi Geetan Manchanda 9911554067

12. Mata Sundari Shashi Kiran (Convenor) 9910212456

13. MH K. V. Shantha 8527367051

14. Rajdhani R.D. Sarma 9871233476

15. Ramjas Ruchika Verma 9212903280

16. Vivekananda Shobha Rani 22142135

17. IP Col W Vagisha Sharma 9910613960

18. MH Lalita Dhar 9811266030

Calculus (2) and Analysis (5) papersConveners : Sachi Srivastava (7838266611)

Shashi Kiran (9910112456)


19. Shivaji Surbhi Madan 9711140225

20. LSR Monika Singh 9953530501

1. Hindu Samridhi Mehta 9868367179

2. IP Col W Gunjan Khurana 9911834999

3. JDM Sushma Bansal 9811014577

4. JMC Indrakshi Dutta 9810646675

5. Keshav Ashish Bansal 9891011050

6. Kamal Nehru Rita Malhotra 9810213881

7. Lakshmi Bai Bina Gupta 9818005667

Algebra (4)Conveners : Kanchan Joshi (9810973349)

Sudesh K. Shah (9810254572)

7. Lakshmi Bai Bina Gupta 9818005667

8. Maitreyi Elizabeth Michael 9891158374

9. MH Ritu Gupta 9810480690

10. PGDAV Savitri Rawat 9818516611

11. Satyawati Renu Jain 9871502102

12. Shivaji Aparna Jain 9868416665

13. SVC Sudesh K. Shah (Convenor) 9810254572

14. St. Stephens Radha Mohan 9818556911

15. SPM Suman Lata 9911545505

16. ZHDC Dhiraj Kr Singh 9868322749

17. Kirori Mal Dinesh Khattar 9810821948

1. ANDC Roopesh Tehri 9818542024

2. ARSD Monica Suri 9811849956

3. DDU Ratnesh R. Saxena (Convenor) 9910100961

4. Dayal Singh Dinesh Kumar 256346355

5. Keshav Arpana Sharma 9810507274

6. Kirori Mal Pratibha Kumar 9350056445

Differential Equations (3)Conveners : R. Panda (27666658)

Ratnesh R. Saxena (9910100961)

6. Kirori Mal Pratibha Kumar 9350056445

7. LSR Mahesh Kumar 9289023205

8. Mata Sundari Gurpreet Kaur 9971556694

9. PGDAV (Eve) Hari Pratap 9717740241

10. Shivaji Mridula Budhraja 9212500143

11. Sh Baghat Singh Renu Rani Gupta 9818880247

12. SGTB Virender Kumar Mehra 9810745604

13. SVC Swarn Singh 9818627285

14. JDM Neelam Sharma 9953766229

1. Hans Raj Arvind 09868016443

2. Hindu Seema Paliwal 9818156736

3. JMC Ambika Bambani

4. Kamla Nehru Pooja 9711397503

5. Lakshmi Bai Asha G. Shankar (Convener) 9811450549

Numerical Methods (1)Conveners : Arvind Patel (9310568439)

Asha G. Shankar (9811450549)

6. Satyawati Vaneeta Goel 9868640384

7. SVC Ranjana Mehta 9711602762, 25282841

1. ARSD Chand Mitro 9810240694

2. Deshabandu Laxmi Bandopadhayay (Convener) 9818563499

3. DDU Sudha Arora 9818057610

4. MH Meetu Bhatia Grover 9811279551

5. Rajdhani Ravi Prakash (Convener) 9810746091

6. Satyawati Monika Mehta 9891940642

Probability and Statistics (1)Conveners : Laxmi Bandopadhayay (9818563499)

Ravi Prakash (9810746091)

7. Sh Baghat Singh Jyoti Varshney 9910580587

1. DRC Seema Khurana 9810330187, 27861273

2. JMC AnuAhuja (Convener) 9811392133

3. Kiroi Mal Reeta Johar 8826469806

4. MH Manjari Srivastava 9899228986

5. Satyawati Vani Sharma 9212205254

6. SGTB Satish Verma 9910050111

Calculus of Variations and Optimization (1)Conveners : C.S. Lalitha (9891196651)

Anu Ahuja (9811392133)

7. Vivekananda Vinay Trehan 9911159530

8. Deshbandhu Laxmi Bandopadhayay 9818563499

1. SVC Shakuntala Wadhwa (Convener) 9873573735

2. LSR Monika Singh 9953530501

3. Hindu Meenal Sambhor 9811939893

4. Kalindi Mohd. Amir 9015835841

5. Kalindi Geetika Khunger 47313366, 9910228099

Number Theory (1)Conveners : Atul Gaur (9850980356)

Shakuntala Wadhwa (9873573735)

1. ANDC Gaurav Sharma 9891987848

2. ARSD Jyoti Kaushik 9810499350

3. Aurbindo Davinder Singh 9818345492

4. Bhaskaracharya Neeru Sharma 9811463962

5. B RAmbedkar Sarla Devi Bhardwaj 9819428322

DC-II (6)

Conveners : C.S. Lalitha (9891196651)

Sarla Devi Bhardwaj (9819428322)

5. B RAmbedkar Sarla Devi Bhardwaj 9819428322

6. Deshbandhu Harindri Chaudhary (Convener) 9868316343

7. DCAC Chaitnya Kumar 9312209181

8. Hindu Sachin Vashishtha 9818427882

9. Gargi Pooja Gupta 996842092,

23550911

10. IP Col W Chander Shekhar 9891918287

11. JDM Sharda Sharma Gautam 9211830004

12. Kalindi Charu Khanna 9811834446

13. Kirori Mal Shiv Kr Kaushik 9818133501

14. Kamla Neh Pragti Gautam 9911037839

15. Maha Raja Ag Anuradha Sharma 9810878134


17. Moti Lal Neh Preeti Upreti 9868913101

18. Ramjas Neelam Lau 9818459531

19. Shyam Lal Balram Kindra 9911805964

DC-II (6)

Cont’d…..

20. SGTB Charanpreet Kaur 9818599201

21. St. Stephen’s Sonia Davar 9873779580

22. ZHPGC (Eve) Qamrul Haque 09897179429

1. Dept. Math. Atul Gaur (Convener) 9850980356

2. CIC Umesh Kumar 9711149636

3. Hans Raj Arvind 9868016443

4. Ramjas Neelima 9818470398

Applied Courses (4)

Conveners : B.K. Dass (9811191046)

Atul Gaur (9819428322)

Specimen of the Course Structure

Analysis I

Total marks: 100

Examination: 75

Internal Assessment: 25

4 Lectures, 1 Presentation,

1 Tutorial (per week per student)

Ist WeekIst Week

The completeness property of R, Boundedness of subsets of R, Suprema, Infima,

Completeness Axiom.

Page 19-22 [1].

IIndWeek

Archimedean property, density of rational numbers in R, characterization of

intervals, Sequences, bounded sequence, unbounded sequences.

Page 23- 24, 31-32[1].


cont’d……

III rd Week

General and Particular terms of Sequence, Limit of a Sequence, Limit

Theorems for Sequences.

Page 33-42, 43-45[1]

IVthWeek

Limit theorems continued.Limit theorems continued.

Page 46-48 [1].

VthWeek

Infinite limits , omitted proofs of Theorems 9.9 and 9.10.

Page 49-52 [1].

VIthWeek

Monotone sequences, monotone convergence theorem, Cauchy Sequences,

subsequences, , Bolzano-Weierstrass theorem for sequences (statement only)

Page 54-55,57,60-61, 63-67, 69-70 [1].


cont’d……VIIth Week

Definition of a subsequencial limit, limsup and liminf, Thm 11.8 omitted.

Page 70-72[1].

VIIIth Week

Definition of infinite series, Graphical Explanations of divergence of \sum 1/n

and convergence of \sum 1/n^2, sequence of partial sums, Cauchy Criterion,

necessary conditions for convergence of infinite series.necessary conditions for convergence of infinite series.

Page 90-93, 100-101[1].

IXth Week

Tests of convergence: comparison test, Ratio test, Cauchy’s nth root test

(proof only for special cases )

Page 94-98[1].

Xth Week

Alternating Series, Integral test (without proof), Alternating Series Theorem,

Page 100-104[1].


cont’d……XIth Week

Continuous functions, sequential criterion of continuity, combinations of

continuous functions and compositions of continuous functions.

Page 115-123[1]

XIIth Week

Properties of continuous functions, the maximum-minimum theorem,

intermediate value Theorem.intermediate value Theorem.

Page 126-128.[1]

REFERENCES:

[1] K. A. Ross, Elementary Analysis: The Theory of Calculus, Undergraduate

Texts in Mathematics, Springer (SIE), Indian reprint, 2004.

[2] R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis (3rd

Edition), John Wiley and Sons (Asia) Pte. Ltd., Singapore, 2002.

4year1

Documents

students presentation

students presentation

cafc foundation course

foundation papers

periodsweek2 lectures

discipline course

periodsweek4 lectures

course idc