# Faculty & Staff By Last Name

## Faculty & Staff By Last Name

# Shuang Zhang

Title: Professor and Department Head

Office: 4114 French Hall

Tel: 513-556-4052

Email: zhangs@ucmail.uc.edu

Web: http://homepages.uc.edu/~zhangs/

Joined the Department of Math Sciences of UC in 1990.

The first recipient of Taft Award for Distinguished Faculty Achievement in 1996.

Taught numerous math courses from high-school level to Ph.D.level since 1978.

Research interests and publications mainly in Operator Algebras/Functional Analysis, a math branch called Morden Analysis.

Research supported by the National Science Foundation during 1989-1999.

Serve as a referee for about 20 math journals with worldwide circulation, for the National Science Foundation, and for some book publishers.

Organized or co-organized 10 math domestics/international conferences/worlshops.

Frequently invited as a main speaker of special sessions of the American Math Society and of domestic/international math conferences.

http://math.uc.edu/~zhangs/index.htm

## Education

- Ph.D. in math, Purdue University, Indiana/USA, 1988 (Functional Analysis, Operator Algebras, C*-Algebras.).
- MS in math, Capital Normal University, Beijing, China, 1982 (Functional Analysis).

## Research Information

### Research Interests

Pure Math: Operator Theory. Theory of C*-algebras and von Neumann

algebras. K-theory. Homotopy Theory. Fredholm Index Theory.

### Research Support

- (PI), Zhang, Shuang,
*Structure of Operator Algebras*, Simons Foundation. (281966), 09-01-2013 to 08-31-2018. Status: Active. - (Collaborator), Halpern, Herbert; Kaftal, Victor; Peligrad, Costel; Weiss, Gary; Zhang, Shuang,
*Collaborative Research: Operator Theory/Operator Algebras, GPOTS 07-08*, National Science Foundation. (DMS-0649960), 04-01-2007 to 03-31-2009. - (Co-PI), Kaftal, Peligrad, Weiss, Zhang,
*2013, Operator Algebras and Applications*, NSF. BAD DATE to BAD DATE. - NSF . (DMS - 9626592), 1997 to 1999.
- NSF . (DMS - 9225076), 1993 to 1997.
- NSF Young Investigator . (DMS-8921369), 1992 to 1993.
- NSF . (DMS - 9002958), 1990 to 1992.
*Several Summers*, Taft Grants -. 1990 to 2009.- NSF . (DMS - 8902371), 1989 to 1991.

## Publications

### Peer Reviewed Publications

- Strict comparison of positive elements in multipler algebras, Canadian J. of Math 69(2017)2, 373 - 407 (joint work with Kaftal and Ng).
- Projections in C*-algebras and strict comparison (joint work with Kaftal and Ng), Operator Theory: The State of Art, Theta, Bucharest, 2016, page 53-74.
- Strict comparison of projections and positive combinations of projections in certain multiplier algebras, J. of Operator Theory, 73(2015), 187 - 210 (joint work with V. KAFTAL and P. W. NG).
- Commutators and linear spans of projections in certain finite C*-algebras, J. Funct. Analysis, 266(2014)4, 1881-1912 (Joint work with Kaftal and Ng)
- Finite sums of projections in von Neumann algebras, Trans. Amer. Math. Soc. 365(2013), 2409 - 2445 (joint work with Halpern, Kaftal, and Ng.)
- Projection decomposition in multiplier algebras, Math. Ann. 352(2012)3, 543--566 (Joint work with V. Kaftal and Ping Ng).
- Finite sums of projections in purely infinite C*-algebras with torsion K0, Proc. Amer Math Soc, 140(2012), 9, 3219 - 3227 (joint work with V. Kaftal and P. Ng)
- Positive combinations and sums of projections in purely infinite simple C*-algebras and their multiplier algebras, Proc. Amer. Math. Soc 139(2011)8, 2735-2746 (joint work with Victor Kaftal and P. W. Ng),
- Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras, SCIENCE CHINA Mathematics, 54(2011)11, 2383 - 2393, (joint work with V. Kaftal and P. Ng)
- Operator-Valued Frames, Trans. Amer. Math. Soc. 361 (2009) 6349-6385. ( Joint with V. Kaftal and David Larson).
- Strong sums of projections in von Neumann factors, J. Funct. Anal, 257 (2009), 2497-2529 (Joint work with V. Kaftal and Ping Ng).
- Operator-Valued Frames on Hilbert C*-modules, Contemporary Math No 451, AMS- SIAM, 2007, 171-185 (Joint work with V. Kaftal and A. Larson).
- Open problems around certain simple C*-algebras and multiplier algebras, Proceedings of the 2007 International Congress of Chinese Mathematicians (ICCM), Vol.1(2007), 674 - 692.
- C*-algebras generated by a projection and the reduced group C*-algebras C*_rZ*Z_n and C^*_rZ_m*Z_n$, Int. J. Math. 16(2005)5, pages 1-22.
- Toeplitz algebras and C*-algebras arising from reduced reduced group C*-algebras.
*Illinois J. Math*,*48(2004)*1, 199-218. - K-theory of certain C*-algebras associated with free products of cyclic groups.
*Journal of Operator Theory*,*45(2001)*, 251-264 (joint with W. Szymanski). - On the homotopy type of the unitary group and the Grassmann space of purely infinite simple C*-algebras.
*K-Theory*,*24(2001)*, 203-225. - Type II1 factors generated by purely infinite simple C*-algebras associated with free groups.
*Proc. Amer. Math. Soc.*,*128(1999)*, 813-818 (Joint with W. Szymanski). - Purely infinite simple C*-algebras arising from the reduced group C*-algebras.
*Contem. Math.*,*228(1998)*, 365-389. - Rectifiable diameters of the Grassmann spaces of von Neumann algebras and certain C*-algebras.
*Pacific J. of Math.*,*177(1997)*, 377-396. - Toeplitz algebras and infinite simple C*-algebras associated with reduced group C*-algebras.
*Math. Scand.*,*81(1997)*, 86-100. - Infinite Simple C*-algebras and reduced cross products of abelian C*-algebras and free groups.
*Manu. Math.*,*92(1997)*, 487-514 (Joint with W. Szymanski). *Quasi-diagonalizing unitaries and the generalized Weyl-von Neumann theorem, Birkhauser Boston, Boston, MA, 1995*.- K-theory and homotopy of certain groups and infinite Grassmann spaces associated with C*-algebras.
*Int. J. Math.*,*3(1994)*, 425-445. - Homotopy of projections and factorization in the unitary group of certain C*-algebras.
*Math. Scand.*,*73(1993)*, 281-306. - Exponential rank and exponential length of operators on Hilbert C*-modules.
*Annals of Mathematics*,*137(1993)*, 129-144. - Factorizations of invertible operators and K-theory of C*-algebras.
*Bull. Amer. Math. Soc.*,*28(1993)*, 75-83. - K-theory and a bivariable Fredholm index.
*Contemporary Math., Amer. Math. Soc.*,*148(1993)*, 155-190. - Certain C_-algebras with real rank zero and their corona and multiplier algebras, Part IV.
*Inter. J. Math.*,*3(1992)*, 309-330. - Certain simple C*-algebras with nonzero real rank whose corona algebras have real rank zero.
*Houston J. Math.*,*18(1992)*, 57-71 (Joint with H. Lin). - Certain C_-algebras with real rank zero and their corona and multiplier algebras, Part II.
*K-Theory*,*6(1992)*, 1-27. - On the exponential rank and exponential length of C*-algebras.
*J. Operator Theory*,*28(1992)*, 337-355. - Certain C_-algebras with real rank zero and their corona and multiplier algebras, Part I.
*Pacific J. Math.*,*155(1992)*, 169-197. - Five problems on the structure of multiplier algebras of real rank zero.
*Contemporary Math., Amer. Math. Soc.*,*120(1991)*, 199-203. - On the ideal structure of generalized Calkin algebras.
*Contemporary Math., Amer. Math. Soc.*,*120(1991)*, 193-198. - On infinite simple C*-algebras.
*J. Funct. Anal.*,*100(1991)*, 221-231 (Joint with H. Lin). - Matricial structure and homotopy type of simple C*-algebras of real rank zero.
*J. Operator Theory*,*26(1991)*, 283-312. - K1-groups, quasidiagonality and interpolation by multiplier projections.
*Trans. Amer. Math. Soc.*,*325(1991)*, 793-818. - Star-shaped sets and fixed point theorems of multivalued mappings.
*Math. Japonica*,*36(1991)*, 327-334. - A Riesz decomposition property and ideal structure of multiplier algebras.
*J. Operator Theory*,*24(1990)*, 209-225. - Diagonalizing projections in the multiplier algebra and matrices over a C*-algebra.
*Pacific J. Math.*,*145(1990)*, 181-200. - TrivialK1-flow of AF and finite von Neumann algebras.
*J. Funct. Anal.*,*92(1990)*, 77-91. - C*-algebras with real rank zero and the internal structure of their corona and multiplier algebras, Part III.
*Can. J. Math.*,*62(1990)*, 159-190. - A property of purely infinite simple C*-algebras.
*Proc. Amer. Math. Soc.*,*109(1990)*, 717-720. - Stable isomorphism of hereditary C*-subalgebras and stable equivalence of open projections.
*Proc. Amer. Math. Soc.*,*105(1989)*, 677-682. - On the structure of projections and ideals of corona algebras.
*Canadian J. Math.*,*41(1989)*, 721-742. - Derivations and (hyper)invariant subspaces of a bounded operator.
*Proc. Amer. Math. Soc.*,*102(1988)*, 261-267. - Centeric sets, star-shaped sets and fixed points.
*Beijing Shiyuan Natural Science Monthly*,*1(1981)*, 102-117. - The minimal ideal in multiplier algebras, accepted by J. of Operator Theory, 79(2018)2, 419-462 2017SS.

### Books

- Bi-variable Fredholm indices of invertible operators, Accepted by Springer-TUP, finalizing.
*Operator Algebras and Operator Theory*. Contem. Math. Book Series, 228 (1998) ,(Edited jointly with L. Ge, H. Lin, Z-J. Ruan, D. Zhang).

## Presentations & Lectures

### Invited Presentations

- (05-2015).
*Plenary speaker at the Workshop on Operator Algebra and Harmonic Analysis, Tsinghua Sanya International Mathematics Forum (TSIMF), Hainan Province, China*. - (08-2014).
*Plenary speaker at the Special Week on Operator Algebras, Shanghai, Eastern Normal University.*. - (07-2014).
*Invited talk at the National Sun Yat-sen University, Taiwen.*. - (04-2014).
*About Joint Programs of Chinese Institutions and US Universities, Beijing, China*. - (04-2014).
*Awarded as Outstanding Alumini Honor and gave invited series lectures at the Capital Normal University, Beijing, China.*. - (07-2013).
*Invited presentation "Operator Algebras and Applications" at the Qufu Normal University, Shangdong, China*. - (06-2013).
*7-lectures on the US education system, Capital Normal University, Beijing, China*. - (06-2013).
*Invited presentation "Profection structure of C*-algebras" at the China Ocean University, Qingdao, China*. - (06-2012).
*Decomposition of positive elements as finite linear combinations of projections*Special week on Operator Algebras, Research Center For Operator Algebras, Shanghai, China. - (06-2012).
*5-Lecture Series on Theory of Operator Algebras and Applications*Capital Normal University, China. - (06-2012).
*K-skeleton Factorization and Fredholm Index*Mathematics Institute of Fudan University, Shanghai/China. - (03-2012).
*About the higher Education System of USA*Central University of Finance and Economics, China. - (03-2012).
*About the Joint 2+2 and 2+3 Program in Math/Stat*Capital Normal University, China. - (03-2012).
*The process of application, admission, and attending University of Cincinnati*Beijing Information Science&Technology University, China. - (08-2011).
*Overview on important research results in Analysis*Colloquium talk, Capital Normal University, Beijing/China. - (07-2011).
*Topology and projections in C*-algebras and multiplier algebras*2011 Operator Algebra Workshop, East China Normal University, Shanghai/China. - (07-2011).
*K-Theory invariants for classifying C*-algebras*Colloquium talk, Capital Normal University, Beijing/China. - (03-2011).
*About non-commutative analysis and topology*Colloquium talk, Beijing Information Science&Technology Univbersity, Beijing/China. - (03-2011).
*Non-commutative topology and non-commutative geometry*Colloquium talk, Capital Normal University, China. - (07-2010).
*Main speaker, International Conference on Operator Algebras*Academy of Mathematics and System Sciences, Beijing/China. - (09-2009).
*Main speaker, the Workshop on classification of C*-algebras.*Qinhuangdao/China. - (05-2008).
*Invited speaker at the American Math Society Meeting No 1039*Claremont/California. - (12-2007).
*Main speaker, the 2007-International Congress of Chinese Mathematicians*Hangzhou/China. - (01-2006).
*Operator-Valued Frames*Operator algebras and applications,of the American Math Society Annual Meeting (Joint work with V. Kaftal and D. Larson, presented by V. Kaftal) . - (07-2005).
*Simple C*-algebras and their multiplier algebras*The First International Operator Algebra and Operator Theory Symposium, Xi’an/China. - (04-2003).
*K-theory of C*-algebras generated by certain reduced group C*-algebras and projections*Operator algebras and free probability, of the American Math Society Meeting, Bloomington, Indiana. - (04-2003).
*Rectifiable diameters of the Grassmann spaces of certain C*-algebras*Operator algebras and applications, of the American Math Society Meeting, Bloomington, Indiana . - (01-2003).
*The contractibility of unitary group of certain purely infinite simple C*-algebras*C*-extensions and classification of C*-algebras, of the American Math Society Meeting, Baltimore, MD. - (11-2002).
*Invariants arising from C*-algebras associated with 0-1 sequences*Wabash Seminar Monthly Series On Functional Analysis. - (08-2002). Satellite Conference of the International Congress of Mathematicians, Operator Algebras and Applications, Chengde, China.
- (06-2002).
*Around a long standing problem on simple C*-algebras*Mathematical Institute of China, Beijing, China. - (06-2002).
*A new approach to K-theory*Morningstar Mathematical Research Center, Beijing, China. - (08-2001). Operator Algebras, of the 2001 Canada-China Initiative In Mathematical Sciences, Vancouver, Canada.
- (07-2001).
*Simple C*-algebras and their invariants*Workshop on Operator Algebras , Shanghai, China. - (03-1999).
*K-theory of certain simple C*-algebras associated with cross products of cyclic groups*Operator spaces and applications, of the American Math Society Meeting (941) , University of Illinois. - (03-1999).
*An overview on invariants of C*-algebras*Annual Conference of the Math Institute of the University of Illinois, Urbana, Illinois. - (01-1998).
*Purely infinite simple C*-algebras generated by a weighted shift and an isometry*Recent progress in the theory of operator algebras and their applications, of the American Math Society Joint Annual Meeting, Baltimore, Maryland. - (12-1997).
*On structure of certain purely infinite simple C*-algebras*The structure and classification of amenable C*-algebras, of the Canadian Math Society Annual Meeting, Victoria, B. C.. - (07-1997).
*K-theory of C*-algebras and its applications*Nanjing University, China. - (07-1997).
*On C*-algebras and their invariants*Operator Algebras and Operator Theory, East China Normal University, China. - (07-1997). Five Lectures on C*-algebras and von Neumann algebras, Nanjing University, China .
- (06-1997).
*K-theory of C*-algebras*Beijing Normal University, China. - (05-1997). Regional Meeting of the American Mathematical Society , Detroit, Michigan.
- (10-1996).
*About the K-theory of certain purely infinite C*-algebras*Annual Wabash Mini conference, IUPUI. - (08-1996).
*Generalized Fredholm index*University of Newcastle, Australia. - (05-1996).
*Structure on infinite simple C*-algebras*24th Annual Canadian Symposium on Operator Algebras and Operator Theory, University of Saskatchewan. - (05-1996).
*Reduced group C*-algebras and associated infinite simple C*-algebras*NSF Annual Conference on Great Plains Operator Theory, Arizona State University. - (07-1995).
*Simple C*-algebras and reduced cross products*Invariants of Operator Algebras, Cork, Ireland. - (06-1995).
*Can simple C*-algebras contain both nonzero finite and infinite projections?*Operator Symposium of Canada, Fields Institute, Waterloo. - (04-1995).
*Toeplitz C*-algebras associated with free products of cyclic groups*University of New York at Buffalo. - (03-1995).
*Simple C*-algebras of real rank zero*Purdue University and Indiana University at Indianapolis. - (10-1994).
*A long standing problem on simple C*-algebras and recent progress*Extramural Modern Analysis Mini conference , Indiana University - Purdue University at Indianapolis. - (06-1994).
*Purely infinite simple C*-algebras generated by one projection and reduced group C*-algebras*Simple C*-algebras, of the American Math Society, University of Oregon, Eugene. - (05-1994).
*Structure of certain simple C*-algebras*Annual Conference on Great Plains Operator Theory , University of Nebraska. - (10-1993).
*C*-algebras generated by reduced group C*-algebras and one a projection*Extramural Modern Analysis Mini conference, Indiana University. - (07-1993).
*K-theory of C*-algebras*Mathematical Institute of the Academic Sinica of China, Beijing, China. - (1993).
*K-Theory and its applications*Department of Mathematics, Indiana University - Bloomington. - (10-1992).
*Rectifiable diameters of von Neumann algebras and certain C*-algebras*Operator Theory and Operator Algebras, of the American Math Society, Wright State University, Dayton. - (08-1992).
*Invited speaker on the Royal Danish Academy of Sciences and Letters/commemorative symposium*Copenhegan/Denmark. - (07-1992).
*K-theory and invertible operators on a Hilbert C*-modules*Texas A& M University. - (05-1992).
*Essential commutant and K-theoretical invariants*NSF Annual Conference on Great Plains Operator Theory, University of Iowa. - (03-1992).
*Homotopy groups of the unitary groups and Grassmann spaces of certain C*-algebras*Operator Algebras, of the conference of the American Math Society, Tuscaluoosa, Alabama. - (03-1992).
*K-theory and homotopy of certain groups and infinite Grassmann spaces associated with C*-algebras*Operator Algebras And Algebraic Topology, of the conference of the American Math Society, Springfield, Missouri. - (02-1992).
*Factorizations of invertible operators and Fredholm index*NSF Wabash Functional Analysis Seminar. - (08-1991).
*Factorizations of invertible operators on Hilbert C*- modules*NSF CBMS-Regional conference Homology and Index Theory. - (05-1991).
*Factorization of unitary elements in C*-algebras*NSF supported Annual Conference on Great Plains Operator Theory, Texas A& M University. - (04-1991).
*A proof for the Phillips-Ringrose conjecture*Wabash Extramural Modern Analysis Mini Conference, IUPUI , Indianapolis, IN. - (01-1991).
*Certain C*-algebras of real rank zero and their multiplier algebras*Non-commutative Topology And C*-Algebras, of the American Math Society Joint Annual Meeting , San Francisco, CA. - (11-1990).
*A Riesz decomposition property and applications*Special session "Operator Theory/ Operator Algebras" of the American Math Society, University of California/Irvine. - (05-1990).
*Ideal structure of generalized Calkin algebras. The Regional Conference on Operator Algebras/Operator Theory*Texas Christian University . - (04-1990). The NSF Great Plains Operator Theory Conference , University of New Mexico.
- (03-1990).
*Quasidiagonal operators on a Hilbert C*-module*Arizona State University. - (03-1990).
*Internal structure of multiplier algebras*University of Georgia. - (02-1990).
*C*-algebras with the FS property*University of Alabama. - (01-1990).
*Some recent results about simple C*-algebras of real rank zero. The American Math Society Joint Annual Meeting*Louisville, KY. - (10-1989).
*Simultaneously quasi-diagonalizing two projections and trivial K1-group*The 852th American Math Society , Muncie, Indiana. - (05-1989).
*K1-group and structure of certain multiplier C*-algebras*The 17th Annual Canadian Symposium on Operator Algebras and Operator Theory, University of Toronto. - (06-1988).
*Quasi-diagonality in multiplier algebras. The Conference on Great Plains Operator Theory*Indiana University -Purdue University at Indianapolis. - (07-2015).
*Plenary speaker at the Workshop on Dynamic Systems and Operator Algebras*Math Institute of Jilin University, China. - (07-2017).
*Invite plenary speaker The 3rd Summer Workshop on Operator Algebras and Noncommutative Geometry*Heibei Normal University, China. - (07-2016).
*Invited plenary speaker at the International conference on structure of C*-algebras and tracial approximation*Heibei Normal University, China. - (12-2017).
*Invited plenary speaker at the International Workshop on Operator Algebras*Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China. - (03-2017).
*Speaker for the Workshop for attending the US Universities*Capital Normal University, China. - (12-2017).
*Generalied Fredholm Index and Applications*Colloquium Talk, ChongQing University. - (12-2017).
*Generalized Weyl-von Neumann Theorem in the multiplier algebras*Colloquium Talk, Chongqing Normal Univeristy. - (12-2017).
*Application of Generalized Fredholm Indices*Colloquium Talk, West-South University . - (12-2017).
*Structure of Multipler Algebras and Index Theory*Colloquium Talk, Zhong Shan University at Zhuhai. - Invited 40-minute talk (07-2018).
*Purely Infinite simple C*-Algebras generated by an isometry and a bilateral shift*IWOTA-2018, Shanghai, China.

## Honors & Awards

- Taft Award for Distinguished Faculty Achievement. , 1996. As the first recipient of this newly established award .

## Experience & Service

### Work Experience

- 2010 to 2020, Department Head,.
- 1997Professor of Math, University of Cincinnati.
- 1993 to 1997, Associate Professor of Math, University of Cincinnati.
- 1990 to 1993, Assistant Professor of Math, University of Cincinnati, Ohio/USA.
- 1988 to 1990, Math Instructor and research, University of Kansas, Kansas/USA.
- 1988 to To Present, as visiting scholar with, Univ. of Copenhagen/Denmark, China Sinica, MorningStart Math Research Institute, Zhejiang University, Univ. of Illinois/Urbana, Univ. of Toronto/Canada, Fields Institute/Canada, Univ. of Victoria/Canada, Capital Normal Univ./China, Beijing Normal Univ./China, Beijing Information & Technology Univ./China, East Normal Univ. /China, Nanjing University/China, Fudan Univ./China, Central Univ. of Finance & Economics/China, Xi'an Normal Univ./China, China Ocean University, QingDao University, QvFu Normal University, Tsinghua Sanya International Mathematics Forum at Sanya, National Sun Yat-sen University in Taiwan,....... .
- 1982 to 1983, Lecturer , Capital Normal University, Beijing/China.
- 1978 to 1980, High School Math Teacher, Xinqiaolu High School, Beijing/China.
- 1996Distinguished Faculty Achievement Award - only one at UC,.

### Events Organized

- Conference. Co-organizer of the GPOTS-2008 (06-2008, University of Cincinnati.
- Co-organizer of the Amer. Math Society Special session (10-2006, Univeristy of Cincinnati.
- Co-organizer of the AMS special session (01-2003, Baltimore/Maryland.
- Co-organizer of the Satellite Conf. of the 2002-ICM (08-2002, Chengde/China.
- Organizer of the C*-Algebra workshop (07-1997, Nanjing/China.
- Organizer of workshop on Operator Algebras (07-1997, Shanghai/China.
- Co-organizer of the 3rd International Conference on C*-algebras (07-1997, Eastern China Normal University.
- Co-organizer of the AMS special session (01-1997, San Diego.
- Co-organizer of the GPOTS-1995 (05-1995, University of Cincinnati.
- Co-organizer of the Annual Meeting of AMS special session (01-1994, Cincinnati Conventional Center.
- Conference. Special Week on Operator Algebras (06-18-2012 to 06-22-2012) , Shanghai, China.

### Service

- Service as a referee for about 20 math journals or publishers
- Math Deptartment - Head Review Committee, 1999
- Math Department - Head Search Committee, 2000
- Math Department - Essentially all kinds of Committees repeatedly, 1990 to To Present
- McMicken College of Arts and Sciences Budget Committee, 2012 to To Present
- Academic Committee Chair, 2012 to To Present
- International 2+2 Joint Program Coordinator, 2011 to To Present
- Online Course Evaluation Coordinator, 2011 to To Present
- A&S Heads Council, 2010 to To Present

### Courses Taught

*Comments:*1990A-2010A - Numerous Math Courses from undergraduate freshman to senior gruduate PhD stuents: Topological vector spaces (Graduate course) at Capital Normal University, Beijing/China. Real Analysis I, II, III. Special Topics in Functional Analysis (for PhD candidates). Advanced Calculus I, II, III. Complex Analysis I, II, III. Calculus I, II, III, IV,. Honored Calc I, II,III. Differential Equations. Linear Algebra I, II. Applied Calculus I, II. Matrix Method and Applications. Discrete Mathematics. Introduction of Abstract Mathematics. Calculus for Biosciences. Intro. Calculus I, II. Abstract Algebra. Finite Math And Application. Topics In Math I, II, III. Finite Math and Calculus. Foundation for Applied Calculus I, II, III. Elementary Statistics and Probability- 15-MATH-505 ADVANCED CALCULUS
*Level:*Both*Term:*11W - 15-MATH-147H EL PROB & STATS H
*Level:*Undergraduate*Term:*11U - 15-MATH-264 CALC & AN GEOM IV
*Level:*Undergraduate*Term:*11A