Starting on Oct 2, I will be teaching Math 246A, the first course in the three-quarter graduate complex analysis sequence at the math department here at UCLA. This first course covers much of the same ground as an honours undergraduate complex analysis course, in particular focusing on the basic properties of holomorphic functions such as the Cauchy and residue theorems, the classification of singularities, and the maximum principle, but there will be more of an emphasis on rigour, generalisation and abstraction, and connections with other parts of mathematics. The main text I will be using for this course is Stein-Shakarchi (with Ahlfors as a secondary text), but I will also be using the blog lecture notes I wrote the last time I taught this course in 2016. At this time I do not expect to significantly deviate from my past lecture notes, though I do not know at present how different the pace will be this quarter when the course is taught remotely. As with my 247B course last spring, the lectures will be open to the public, though other coursework components will be restricted to enrolled students.

### Recent Comments

### Articles by others

- Andreas Blass – The mathematical theory T of actual mathematical reasoning
- Gene Weingarten – Pearls before breakfast
- Isaac Asimov – The relativity of wrong
- Jonah Lehrer – Don't! – the secret of self-control
- Julianne Dalcanton – The cult of genius
- Nassim Taleb – The fourth quadrant: a map of the limits of statistics
- Paul Graham – What You'll Wish You'd Known
- Po Bronson – How not to talk to your kids
- Scott Aaronson – Ten signs a claimed mathematical proof is wrong
- Tanya Klowden – articles on astronomy
- Timothy Gowers – Elsevier — my part in its downfall
- Timothy Gowers – The two cultures of mathematics
- William Thurston – On proof and progress in mathematics

### Diversions

- Abstruse Goose
- BoxCar2D
- Factcheck.org
- FiveThirtyEight
- Gapminder
- Literally Unbelievable
- Planarity
- PolitiFact
- Quite Interesting
- snopes
- Strange maps
- Television tropes and idioms
- The Economist
- The Onion
- The Straight Dope
- This American Life on the financial crisis I
- This American Life on the financial crisis II
- What if? (xkcd)
- xkcd

### Mathematics

- 0xDE
- A Mind for Madness
- A Portion of the Book
- Absolutely useless
- Alex Sisto
- Algorithm Soup
- Almost Originality
- AMS blogs
- AMS Graduate Student Blog
- Analysis & PDE
- Analysis & PDE Conferences
- Annoying Precision
- Area 777
- Ars Mathematica
- ATLAS of Finite Group Representations
- Automorphic forum
- Avzel's journal
- Blog on Math Blogs
- blogderbeweise
- Bubbles Bad; Ripples Good
- Cédric Villani
- Climbing Mount Bourbaki
- Coloquio Oleis
- Combinatorics and more
- Compressed sensing resources
- Computational Complexity
- Concrete nonsense
- David Mumford's blog
- Delta epsilons
- DispersiveWiki
- Disquisitiones Mathematicae
- Embûches tissues
- Emmanuel Kowalski’s blog
- Equatorial Mathematics
- fff
- Floer Homology
- Frank Morgan’s blog
- Gérard Besson's Blog
- Gödel’s Lost Letter and P=NP
- Geometric Group Theory
- Geometry and the imagination
- Geometry Bulletin Board
- George Shakan
- Girl's Angle
- God Plays Dice
- Good Math, Bad Math
- Graduated Understanding
- Hydrobates
- I Can't Believe It's Not Random!
- I Woke Up In A Strange Place
- Igor Pak's blog
- Images des mathématiques
- In theory
- James Colliander's Blog
- Jérôme Buzzi’s Mathematical Ramblings
- Joel David Hamkins
- Journal of the American Mathematical Society
- Kill Math
- Le Petit Chercheur Illustré
- Lemma Meringue
- Lewko's blog
- Libres pensées d’un mathématicien ordinaire
- LMS blogs page
- Low Dimensional Topology
- M-Phi
- Mark Sapir's blog
- Math Overflow
- Math3ma
- Math3ma
- Mathbabe
- Mathblogging
- Mathematical musings
- Mathematics Illuminated
- Mathematics in Australia
- Mathematics Jobs Wiki
- Mathematics Stack Exchange
- Mathematics under the Microscope
- Mathematics without apologies
- Mathlog
- Mathtube
- Matt Baker's Math Blog
- Mixedmath
- Motivic stuff
- Much ado about nothing
- Multiple Choice Quiz Wiki
- MyCQstate
- nLab
- Noncommutative geometry blog
- Nonlocal equations wiki
- Nuit-blanche
- Number theory web
- Online Analysis Research Seminar
- outofprintmath
- Pattern of Ideas
- Pengfei Zhang's blog
- Persiflage
- Peter Cameron's Blog
- Phillipe LeFloch's blog
- ProofWiki
- Quomodocumque
- Ramis Movassagh's blog
- Random Math
- Reasonable Deviations
- Regularize
- Research Seminars
- Rigorous Trivialities
- Roots of unity
- Science Notes by Greg Egan
- Secret Blogging Seminar
- Selected Papers Network
- Sergei Denisov's blog
- Short, Fat Matrices
- Shtetl-Optimized
- Shuanglin's Blog
- Since it is not…
- Sketches of topology
- Snapshots in Mathematics !
- Soft questions
- Some compact thoughts
- Stacks Project Blog
- SymOmega
- Tanya Khovanova's Math Blog
- tcs math
- TeX, LaTeX, and friends
- The accidental mathematician
- The Cost of Knowledge
- The Everything Seminar
- The Geomblog
- The L-function and modular forms database
- The n-Category Café
- The n-geometry cafe
- The On-Line Blog of Integer Sequences
- The polylogblog
- The polymath blog
- The polymath wiki
- The Tricki
- The twofold gaze
- The Unapologetic Mathematician
- The value of the variable
- The World Digital Mathematical Library
- Theoretical Computer Science – StackExchange
- Tim Gowers’ blog
- Tim Gowers’ mathematical discussions
- Todd and Vishal’s blog
- Van Vu's blog
- Vaughn Climenhaga
- Vieux Girondin
- Visual Insight
- Vivatsgasse 7
- Williams College Math/Stat Blog
- Windows on Theory
- Wiskundemeisjes
- XOR’s hammer
- Yufei Zhao's blog
- Zhenghe's Blog

### Selected articles

- A cheap version of nonstandard analysis
- A review of probability theory
- American Academy of Arts and Sciences speech
- Amplification, arbitrage, and the tensor power trick
- An airport-inspired puzzle
- Benford's law, Zipf's law, and the Pareto distribution
- Compressed sensing and single-pixel cameras
- Einstein’s derivation of E=mc^2
- On multiple choice questions in mathematics
- Problem solving strategies
- Quantum mechanics and Tomb Raider
- Real analysis problem solving strategies
- Sailing into the wind, or faster than the wind
- Simons lectures on structure and randomness
- Small samples, and the margin of error
- Soft analysis, hard analysis, and the finite convergence principle
- The blue-eyed islanders puzzle
- The cosmic distance ladder
- The federal budget, rescaled
- Ultrafilters, non-standard analysis, and epsilon management
- What is a gauge?
- What is good mathematics?
- Why global regularity for Navier-Stokes is hard

### Software

### The sciences

### Top Posts

- Boosting the van der Corput inequality using the tensor power trick
- Career advice
- The Euler-Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation
- Does one have to be a genius to do maths?
- About
- When is correlation transitive?
- On writing
- Books
- There’s more to mathematics than rigour and proofs
- 246B, Notes 4: The Riemann zeta function and the prime number theorem

### Archives

- February 2021 (6)
- January 2021 (2)
- December 2020 (4)
- November 2020 (2)
- October 2020 (4)
- September 2020 (5)
- August 2020 (2)
- July 2020 (2)
- June 2020 (1)
- May 2020 (2)
- April 2020 (3)
- March 2020 (9)
- February 2020 (1)
- January 2020 (3)
- December 2019 (4)
- November 2019 (2)
- September 2019 (2)
- August 2019 (3)
- July 2019 (2)
- June 2019 (4)
- May 2019 (6)
- April 2019 (4)
- March 2019 (2)
- February 2019 (5)
- January 2019 (1)
- December 2018 (6)
- November 2018 (2)
- October 2018 (2)
- September 2018 (5)
- August 2018 (3)
- July 2018 (3)
- June 2018 (1)
- May 2018 (4)
- April 2018 (4)
- March 2018 (5)
- February 2018 (4)
- January 2018 (5)
- December 2017 (5)
- November 2017 (3)
- October 2017 (4)
- September 2017 (4)
- August 2017 (5)
- July 2017 (5)
- June 2017 (1)
- May 2017 (3)
- April 2017 (2)
- March 2017 (3)
- February 2017 (1)
- January 2017 (2)
- December 2016 (2)
- November 2016 (2)
- October 2016 (5)
- September 2016 (4)
- August 2016 (4)
- July 2016 (1)
- June 2016 (3)
- May 2016 (5)
- April 2016 (2)
- March 2016 (6)
- February 2016 (2)
- January 2016 (1)
- December 2015 (4)
- November 2015 (6)
- October 2015 (5)
- September 2015 (5)
- August 2015 (4)
- July 2015 (7)
- June 2015 (1)
- May 2015 (5)
- April 2015 (4)
- March 2015 (3)
- February 2015 (4)
- January 2015 (4)
- December 2014 (6)
- November 2014 (5)
- October 2014 (4)
- September 2014 (3)
- August 2014 (4)
- July 2014 (5)
- June 2014 (5)
- May 2014 (5)
- April 2014 (2)
- March 2014 (4)
- February 2014 (5)
- January 2014 (4)
- December 2013 (4)
- November 2013 (5)
- October 2013 (4)
- September 2013 (5)
- August 2013 (1)
- July 2013 (7)
- June 2013 (12)
- May 2013 (4)
- April 2013 (2)
- March 2013 (2)
- February 2013 (6)
- January 2013 (1)
- December 2012 (4)
- November 2012 (7)
- October 2012 (6)
- September 2012 (4)
- August 2012 (3)
- July 2012 (4)
- June 2012 (3)
- May 2012 (3)
- April 2012 (4)
- March 2012 (5)
- February 2012 (5)
- January 2012 (4)
- December 2011 (8)
- November 2011 (8)
- October 2011 (7)
- September 2011 (6)
- August 2011 (8)
- July 2011 (9)
- June 2011 (8)
- May 2011 (11)
- April 2011 (3)
- March 2011 (10)
- February 2011 (3)
- January 2011 (5)
- December 2010 (5)
- November 2010 (6)
- October 2010 (9)
- September 2010 (9)
- August 2010 (3)
- July 2010 (4)
- June 2010 (8)
- May 2010 (8)
- April 2010 (8)
- March 2010 (8)
- February 2010 (10)
- January 2010 (12)
- December 2009 (11)
- November 2009 (8)
- October 2009 (15)
- September 2009 (6)
- August 2009 (13)
- July 2009 (10)
- June 2009 (11)
- May 2009 (9)
- April 2009 (11)
- March 2009 (14)
- February 2009 (13)
- January 2009 (18)
- December 2008 (8)
- November 2008 (9)
- October 2008 (10)
- September 2008 (5)
- August 2008 (6)
- July 2008 (7)
- June 2008 (8)
- May 2008 (11)
- April 2008 (12)
- March 2008 (12)
- February 2008 (13)
- January 2008 (17)
- December 2007 (10)
- November 2007 (9)
- October 2007 (9)
- September 2007 (7)
- August 2007 (9)
- July 2007 (9)
- June 2007 (6)
- May 2007 (10)
- April 2007 (11)
- March 2007 (9)
- February 2007 (4)

### Categories

- expository (288)
- tricks (11)

- guest blog (10)
- Mathematics (813)
- math.AC (8)
- math.AG (41)
- math.AP (112)
- math.AT (17)
- math.CA (175)
- math.CO (179)
- math.CT (7)
- math.CV (37)
- math.DG (37)
- math.DS (83)
- math.FA (24)
- math.GM (12)
- math.GN (21)
- math.GR (86)
- math.GT (16)
- math.HO (12)
- math.IT (13)
- math.LO (50)
- math.MG (43)
- math.MP (28)
- math.NA (23)
- math.NT (179)
- math.OA (22)
- math.PR (101)
- math.QA (6)
- math.RA (40)
- math.RT (21)
- math.SG (4)
- math.SP (48)
- math.ST (8)

- non-technical (164)
- admin (45)
- advertising (42)
- diversions (4)
- media (13)
- journals (3)

- obituary (15)

- opinion (31)
- paper (216)
- question (123)
- polymath (85)

- talk (67)
- DLS (20)

- teaching (188)
- 245A – Real analysis (11)
- 245B – Real analysis (21)
- 245C – Real analysis (6)
- 246A – complex analysis (11)
- 246B – complex analysis (5)
- 246C – complex analysis (5)
- 247B – Classical Fourier Analysis (5)
- 254A – analytic prime number theory (19)
- 254A – ergodic theory (18)
- 254A – Hilbert's fifth problem (12)
- 254A – Incompressible fluid equations (5)
- 254A – random matrices (14)
- 254B – expansion in groups (8)
- 254B – Higher order Fourier analysis (9)
- 255B – incompressible Euler equations (2)
- 275A – probability theory (6)
- 285G – poincare conjecture (20)
- Logic reading seminar (8)

- travel (26)

additive combinatorics
almost orthogonality
announcement
approximate groups
arithmetic progressions
Ben Green
Cauchy-Schwarz
Cayley graphs
central limit theorem
Chowla conjecture
compactness
compressed sensing
correspondence principle
distributions
eigenvalues
Elias Stein
Emmanuel Breuillard
entropy
equidistribution
ergodic theory
Euler equations
expander graphs
exponential sums
finite fields
Fourier transform
Freiman's theorem
Gowers uniformity norms
graph theory
Gromov's theorem
GUE
hard analysis
Hilbert's fifth problem
hypergraphs
incompressible Euler equations
inverse conjecture
Kaisa Matomaki
Kakeya conjecture
Lie algebras
Lie groups
Liouville function
Littlewood-Offord problem
Maksym Radziwill
Mobius function
multiple recurrence
Navier-Stokes equations
nilpotent groups
nilsequences
nonstandard analysis
parity problem
politics
polymath1
polymath8
Polymath15
polynomial method
polynomials
prime gaps
prime numbers
prime number theorem
random matrices
randomness
Ratner's theorem
regularity lemma
Ricci flow
Riemann zeta function
Roth's theorem
Schrodinger equation
sieve theory
structure
Szemeredi's theorem
Tamar Ziegler
ultrafilters
universality
Van Vu
wave maps
Yitang Zhang

### The Polymath Blog

- Polymath projects 2021 20 February, 2021
- A sort of Polymath on a famous MathOverflow problem 9 June, 2019
- Ten Years of Polymath 3 February, 2019
- Updates and Pictures 19 October, 2018
- Polymath proposal: finding simpler unit distance graphs of chromatic number 5 10 April, 2018
- A new polymath proposal (related to the Riemann Hypothesis) over Tao’s blog 26 January, 2018
- Spontaneous Polymath 14 – A success! 26 January, 2018
- Polymath 13 – a success! 22 August, 2017
- Non-transitive Dice over Gowers’s Blog 15 May, 2017
- Rota’s Basis Conjecture: Polymath 12, post 3 5 May, 2017

## 29 comments

Comments feed for this article

14 September, 2020 at 2:27 pm

Pedro M. SilvaDear prof. Tao,

(I hope this comment finds you well during these strange times.)

Thank you so much for providing open access to such nice classes.

Unfortunately, due to the difference in time zones, I won’t be able to follow the course.

Nonetheless, I was wondering if you are aware of any other professors or universities giving access to their online courses in math subjects for this semester/quarter. I couldn’t really find any others, except for past courses (which are recorded). Maybe we could collect this info somewhere, as this kind of initiative really helps during these quarentine moments.

In any case, thank you so much.

14 September, 2020 at 7:47 pm

Prateek P KulkarniDear Pedro,

Does ‘open access’ mean we can join the lectures too via zoom link?

‘Cause I have been wanting to take such a course (from a long time)..

16 September, 2020 at 9:06 am

AnonymousYes. You can join via zoom link.

14 September, 2020 at 4:15 pm

EdgawlietHello, where can I (not a student) enrol/take the course?

14 September, 2020 at 7:17 pm

HulkA small typo in the first sentence : departmeht departement. Do you teach about the 1966 Fields medalist A. Grothendieck contribution and more precisely about Grothendieck theorem (or inequality and its recent applications in theoretical computer science and graph theory) and Grothendieck real and complex constants introduced in his famous Résumé of 1956 and whose exact values still remain unknown and open problem problems nowadays (to the best of out knowledge and belief) despite a lot of old and recent research works both in maths and quantum physics which focused on finding and computing their lower and upper bounds (e.g., for the upper bound in the real case, cf. the works of Krivine in 1971 and of Braverman, Makarychev, Makarychev and Naor in 2011) ?

14 September, 2020 at 7:39 pm

Prateek P KulkarniSir, can non-UCLA students join the lectures (the zoom meeting mentioned on course website)? I am very much wanting to take this course sir. I very much look forward to this Complex Analysis course. Please let me know sir…

16 September, 2020 at 9:05 am

AnonymousYes. Anyone can attend the lectures.

14 September, 2020 at 11:32 pm

RyanTerry, have you looked at Marshall’s new text on the subject? – it seems like a very interesting text with a sweeping breadth of problems. Was wondering also what others think of it.

Warmly,

Ryan

21 September, 2020 at 7:34 am

ACSome blog with high visibility should make a page collecting all online resources for various math classes especially videos. There is probably a lot of them out there that we don’t know about, like this one https://www.youtube.com/channel/UCIyDqfi_cbkp-RU20aBF-MQ

5 October, 2020 at 7:33 pm

termino olavendo it! do a good job it won’t be a problem getting blog and other publicity.

27 September, 2020 at 6:45 pm

Sai GopalWhere do I find the zoom meet link to join the public lecture ?

29 September, 2020 at 9:09 am

AnonymousCheck the course link Prof. Tao provided. It is there.

28 September, 2020 at 4:30 pm

AnonymousHello Prof. Tao,

Are the homeworks going to be from Stein and Shakarchi? Also, another related question is, will any of the homeworks be based on your notes?

Thank you,

15 October, 2020 at 3:34 pm

Sabino LamonacaCan anyone tell me what kind of argument would this be? For personal interest only

3 October, 2020 at 2:24 pm

SandyHello,

I am a non-UCLA student who is excited to audit this course. Unfortunately, I was traveling during the first class meeting yesterday, so I was wondering if it is still possible to follow the material having missed the first lecture.

I also wanted to ask whether there is any way for me to watch a recording of Friday’s class (of course I fully understand if the answer is no, since I am not UCLA-affiliated).

Thanks for your time,

Sandy

4 October, 2020 at 5:32 pm

Terence TaoDue to UCLA privacy rules, video recordings can only be hosted on university-hosted platforms such as CCLE, which are restricted to enrolled students.

6 October, 2020 at 9:02 am

AnonymousUnderstood, thanks.

5 October, 2020 at 5:50 pm

DNo zoom link on the UCLA official page. Any help, anyone? Thanks!

5 October, 2020 at 7:36 pm

termino olavenit’s linked to the linked page–“course description”

7 October, 2020 at 11:13 am

AnonymousDear Prof. Tao:

If the pen keeps frozen in OneNote, maybe you can try using Notability. It works well. Also, the notes you use in class is not up to date as the ones you posted on line. The one on line has less errors :-)

14 October, 2020 at 11:10 am

AnonymousNot to promote Apple, but Mac, iPad, and Apple pencil all works much better.

8 October, 2020 at 9:09 am

ChristianCan non UCLA students attend the discussion session on Thursday?

12 October, 2020 at 12:26 pm

Ben JohnsrudeYes, I’m fine with non-UCLA students attending the Thursday discussion, although priority will be given to enrolled students when it comes to answering questions. – Ben

9 October, 2020 at 2:07 am

Sabino LamonacaThis Is so interesting! Thanks

11 November, 2020 at 10:22 am

AnonymousI was not admitted to the Zoom room today. Is it because there is no class at UCLA due to Veterans Day holiday?

11 November, 2020 at 10:35 am

AnonymousWill there be any class on Friday (Nov 13, 20)?

The class page (https://ccle.ucla.edu/mod/page/view.php?id=3173126) marks the schedule for this week as “Week 6 (Nov 9-15)”, not “Week 6 (Nov 9-13)”. Will there be any class on Nov 15?

11 November, 2020 at 11:07 am

Ben JohnsrudeThere will be class this Friday. – Ben

11 November, 2020 at 10:47 am

AnonymousThis also happened to me. I was stuck in the waiting room for the entire hour.

I also had problems with being stuck in the waiting room for the previous two lectures as well (I left and rejoined and was admitted automatically, but that didn’t work this time).

11 November, 2020 at 11:06 am

Ben JohnsrudeYes, there was no lecture today due to Veteran’s day. We’ll reconvene on Friday. – Ben