Wolfram Blog
Jamie Peterson

Online Enrichment with Free Daily Study Groups

November 10, 2020 — Jamie Peterson, Senior Training & Online Learning Manager, Wolfram U

Online Enrichment with Free Daily Study Groups

Students are spending countless hours online for classes this year, pushing educators to offer more engaging and worthwhile virtual content. We debuted Wolfram Daily Study Groups in early April with this in mind, and the results have far surpassed our expectations! Throughout this ongoing program, we’ve been able to keep students, professionals and lifelong learners engaged and connected in an enriching online community. With several Study Groups completed, and more in the works, we thought we’d share some of our successes so far.

How Do Study Groups Work?

The idea is pretty simple: one- to four-week topical programs made up of daily hourlong sessions Monday through Friday. Study Groups feature fun, directed, incremental learning resources. An instructor guides each session by sharing lesson videos, polling the group to review key concepts, introducing practice problems and answering questions.

Highly motivated attendees can demonstrate their newly honed skills by completing autograded quizzes (deployed to the Wolfram Cloud, of course!) and earn certificates of completion. To date, four hundred Study Group participants have earned these certificates that can be shared on college applications, resumes and CVs and posted to LinkedIn profiles.

Start at the Beginning: Introduction and Fundamentals

Our inaugural Study Group started with—you guessed it—a primer on the Wolfram Language. Video lessons were borrowed from Stephen Wolfram’s course An Elementary Introduction to the Wolfram Language. During progressive daily sessions over four weeks, participants built skills by writing their first programs in the Wolfram Language, doing computations and visualizing data. Our poll results showed that different members of the group had a range of plans for their new skills:

How would you like to use the Wolfram Language?

Rory Foulger, instructional designer and technologist in our Outreach & Communications department, led this Study Group, bringing practical teaching experience from various Wolfram student outreach programs. Each week on Friday, Rory introduced fun mini-project activities that provided a recap of topics from that week. In one of the projects, the group applied what they had learned about defining variables and manipulating lists in the Wolfram Language to generate random slot machine (AKA fruit machine) results:

fruits
&#10005

fruits = {\!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
1:eJzFWglYlOe5HTUuIaLINmyzw7DvOwoiCO4YtUbjlrgkLmnMjdqkN01jjLG1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"], {{0, 50}, {50, 0}}, {0, 255},

ColorFunction->RGBColor],
BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->{50., Automatic},
ImageSizeRaw->{50, 50},
PlotRange->{{0, 50}, {0, 50}}]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
1:eJztmgdYlWeWx5ns7uxOyU52kh2TySRRxw4qWEEFpKkoXQE7KCh2ERS7WFAh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"], {{0, 50}, {50, 0}}, {0, 255},
ColorFunction->RGBColor],
BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Automatic,
ImageSizeRaw->{50, 50},
PlotRange->{{0, 50}, {0, 50}}]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
1:eJzNWQlYT2n7PmPm8v+G8TEUKvuWkijVr0VpU9lCZIloE6GUjC0jYxlLH7Iv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"], {{0, 50}, {50, 0}}, {0, 255},
ColorFunction->RGBColor],
BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Automatic,
ImageSizeRaw->{50, 50},
PlotRange->{{0, 50}, {0, 50}}]\), \!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
1:eJzFWgd8FWW+HXmKyupKh4AgRWkSqRKCgkhoCqtIl6JGepEuAST03kF6CiGB
QEhIT0gjIRUC6YT0HhLSK+nlvPPdmRsSxLdvXcX5/Q4zd+6db8759xnS/cfV
Uxc3kyRp/Rv8Z6qu3ufr1uluntaSH2asWr9syapFC79YtWHRkkXrhv/4Pzw5
WMGrBP7Erba2tsnn4uIi5OXlqvC07GnD+bq6OhX+zk3cv76+/jfn1RrKK8pg
42uMFecmQGeDBrQXt8GIRW0w+ee+0L+wHIEh/g3X1NTUvHCtl7mp7y/2ag2B
4X7YaDYHWita4oNpEnoTfadL6MN9nykSPuSx9oJO2HlmI9IfpzesJa5/2XqS
EhPw9Gmp6rixb1wCbbDuki5G/NgL/b6VoDlPQn9Cc76Ej+byeA6Peb4fNfWb
KWHM4h4wND+J8vLyl8ZdbW/bq5dgtHsZDI7uQEVFRcN35s7G2G6yBpPXaGP4
4ncwSFfCwO8lDPqu0V7ooa4Bc2UILX2IiUv649pNU+Tn5//lPlHnpJuDFZbM
0MEm3amwNDNBcUkxTtgcx9qLKzBj+wSMXNcLHy5ujp7U0Xsh7b9UwpCVzaG9
6h/4dM3b+GT12xi++p8YtPw19F/EmFvA3xFDlks4aLzppeRL41p08pg+1syf
gi36S7HjZ01s0v8MK7ePwIotvbBxSzsc2NEaBoe6wuJUX9ifHQhng8FwMRwC
Z6OPYW84CFfO9sH+Y52wal8znDBdjMjY8Ia1/yotjfO4rKwM5g6m2G3/E35a
ponb5/qj1FFCzR0JZUS9H8v4XeIeEUD4NQd8WgLe7QGv7oBnL8BDkxhE52qj
5tZolN9ZgdQ7x5D00IOx+ixX/sy63Hgtn3uemL9/AvSsZmPXrZUwOUCeMUQB
kafsc4ksIoNII5KJxH8CcZ35225AZDfUhXVFdVBnVAV0QpVPN1R59gbuDOMN
xqHMeyke+t2gT6pV93y+H/2RTb1GVVUVDpjoYcAaCbOPD8eFoF046rIRBjsl
FHqQ52MiR9GQq2jKbUZ04TFtnzeCx2P4m7FA5jjq43HiJ9Q1APUPu6P2wXuo
8u+FMo/eqHQbDPiOQ12AHlJiw/5rLSJGxZaYHIcFR3UwcLWEj9dK0LOZiZsJ
RthtuxQXdkjIcSHn9Eb+ECikhkLavnAoUETOhZO4n0HM5fE8IJ/7nJn02VdA
yueoj+2Huoj3UBvcE9W+fVHqOgAVLtR5dyaSgh3+sBb1NR537fH1we4YSj8M
+EmCzi4JJg8P4VrkGeyzX4VTWyVkOSvxo9ZRSBQxJ4o+5FDyKTGB+BoomUUs
4PEyfkcULqUefs6aTX9+ifqkj1EX1Rs1YcTdvij3HIhCB23m2HRE+11pYtv/
RINdgDHGbuc8sfZNaK1nH14lYanZaFgmnMXV8JM47r4dx/UlpNuSd4oST0JH
kaKjmPFU8hnxJTGVoB9KFvP8KmIt6ovWo75wNa9Zwmvpn8zJXGcY6mM0URuu
iaq7/VVa8hxGU8scxAbe/H/7paHXBZniX8daYdS6jhi1uQW0NkgYvkXCHvel
1HEG1yJO45T3IRylf2LMyTueyH5eR79n/ij5Biid30QHijZQC1Gwhn5ZSC3f
Ugt/mzwUdTEDURM+AJV3B+KphxaybXk+aCHiI3z/rRb1d5FxwZh+si1Gre6M
cfpt8fkW9q6NEr463B5H/NbgasxxXAk9icOee3Bgr4QgA/J+pNSnfHVcCfQg
RH7QnsXMg+I5hIir5TxH7kXrZBRQU8FKXqtLLdO4Dn3IGKuNHojqsMEo8/sY
Ba6fIctmCuoC1yMnO1PVB15Uk9Xnq6oqse7GaHy2XgNjt3bEuF/aYaz+Oxj5
iwRd9q+D/ithGnUQFwP34Ren1dixW4LvKfaMECVHchUdKrBWFfaVc72QuV5E
nxTTJ0X0SRF5F62S9RQKHYyv/EXMMeZ+tg7X0kZ9wlDUPBqCiqChKPb6BNn2
X6D41vfI9D38uz5R54+170V8cbANdH7uBB2hYWs7jGeOfL5dwlrLL6ljOXUc
wimfrVhuMRubqMP9iMRYVvpEjuITEV/5Hbhn38tnnuSzNxSQXyHtXfgdQc6F
zPWCFQqWKf5gTctmDD1mPCYPR12cFqoitFDqr4181zHIuDkNdX7LEX3f6YVa
hD8qKyuwykoLn23oDJ2tHVQaxm1rg/E7W2H83ma0/xzs91+KKzFHcMhjPb6/
PB4/Mz+c9kko9VVyJKtR/1CBtTevDzGQPNlD8smxgDlfMFfmXbBQrln51JbP
uMv9RtaRMVLlEyRqoSZKC+VBw1F4exSeOHyJDOtvVfGVn5f9wvi6H+WFKWc4
yzGmdLa2Zjy1xQT6YuLOf2DK0dbYeVsXe/x+xJXo49huvxBTLw7CBvZBeyJf
9MIoJbaylJwXvsmhT3Lok1zGVy7jK28U+U4kphDTCdbcPOZ33iw5N3LYZ56M
kf0hdCRpMeeHoTJ0GEp8hiPHmT6xnoYKjwWI9zn3Qp8YeW3HxN0doLNJxFQb
VY5P3EEtu17BvAt9scPzB+z104VxxH4sM/0Sk892wcZtEm4SWbfIOYxIUnq7
yPknak0dCeZ8dn/y1JL7ei615LEe506WIfhnjZc1iDwXOlL526ShqI8bgurw
ISjzZ767jUSm3SSkW1O/32JkpCeruDf2yS+X50JnmwbGbGGO67dWYqo9xjN2
Vlwbhc3u03Hw7lIcC9iAWacHYvK5N7FFT4Ile0iqPfneV2atZMUv6Y00ZbAO
Z3YiT8ZYNufDLMZYFmMniz37CTlncp9B+6cPJ5hLaVqq+ovEIez1A1iDNVHB
GlzkORzZjmOpQ/hkPpL8zjXJb7GtOzcdY/Q70hcaKl+MV3RMZG5ssP8XVjuP
xdHAVdjiPBeTj3THtPMSdq6kDtaApJucd/3JN4KIU/wiemOqgjS1Ns4r6e3I
+X2Cs2EG4y2d2tL6ykilz1JYF5I+ogb2nzieY4+vDe+DivuaKPb+GLkuo5Fh
NxlPOB/Vs+48LS1pyHGxrT87iz6ghl86y3VqG/OczxBfMTfWO07CCs4I+wOW
YrH5SIw/2gHzf5Vw4EfGFf0VbyFx9ibPICVPYokEMecqmpKfg9CY8ibxDj+3
IDjTJ7NOJ7MuJFFjAvdx7wHRXVEf2R114T1R+eADPPUbjDz3Eciwn4C0m6wX
PnOQGOHTJE82XZzHGivrGM96NX4ba9b2Fph9vieW2Ghhmd1gbHKbjhlnemH8
r63xE2f2E3yOs9kr9/Ri5nqteN4IbaQlTqljak1qPP85kX5KpK4EPqfEteG1
9Fk095EdUB+hgZrQd6mjG+uvJmvKMGQ6jGFsTeEsOQcpfqebxNZhqzWYuKsL
xm0RcdWetaqDqlbNMeqDedc7YZGtJhZZajOmNDDp/CvYxTnlzDIJttQRdYU1
i3NvpY+SJ2FKj49Wcia2EeJ+B7HKb2MUOzx6jTPwa9TQClVB7VAe+C5K/Hoj
//YQZDiMRKr1JOTYzkAx87VxXNlwLpzCuB/HeiV0jBc69ryD2SbvYSZ5/mD1
PmYbd1XF1LfMjdOcgS9wjrdn/3h4WWL+8XnwtoRqfyW+hJZIRU9UI0Sref4+
6nldHXOthmtUBbdgbrRA6d22KPbtiTyPfki3G4Zkq7F4bDUFlXeWorzR+72E
lGjoXv6QfbADdXTEBGLS/raYYdISM69K9ElXfHO2LUafbAO94xLMqMGE9cpp
v4TwSxJzj89UrvKzrSq+HihaHip6GuPhM9RHPIPgXhtO/kQ1Z50K2qMskH2W
6xX7tUTBnbbIcfsAaXYDkWg5BknXJqHeez6yM5Ia6q/wy2HnJaq4mqAvcqQj
JnM2nGnaHLOvvYHZV/j5OHH2dVwid4tNEsw5d906KCHUSEIKa1Yun0WK3Znz
3uTCWaX+gZIv4Uote6jsBe9wGXUC1FtL1IQK+xPkX874LOMzfgk1FHG9Aton
x+NtZLp0QYptf9aWTxF79QvUuM9A/KMHTXLdk89eM0++j7F6XTCRWqacaos5
5i0w91obzDRuhzEnO2LzhdfhyViyYv+zYs11PSwh+KKERNasJ+wj+eyJJcz5
Ct67mlpqac86cqsLVTg/x7uGdq9WuFdSd3mgzL/0rvABfcycy/Ni3HLNTOZg
muPbSLDuwdoyFFFm4/gcPAuPQnwbckRAzLt6FlMwdnMnfLG9K6ZeaIt5FkJL
B3x9rhO+MWgHjzOt4H+I8bSHucE58TbnxAcXJMQx9h5by3lSwPuVMFfKqKWS
+VJNXjXkWB0k81ZxD3nGveK+zP8puZfw90UK/3zyz+E6T7jeYyf2Wwf2Kj63
xVp1wqMrA5mXOii9NQuRQd6/mXntvM0w/cj7mLitC7411cB3N7pglkkXTDfX
gMXV7og7oYGAExK86Ac3xtedYxLun2PNMmVsWdJmzJNs3rPAVa7FTxkP5Zwj
KxkfldRTEfgMats38OfvCrxk++e4K/zp3zTyTyX/BBvai/Ebdb0dws16I8x4
JIodZyIm/G6DDvWMkpObhYUGI1hzNaBr2RPzzbthnn0nXPfRR47FVCSc74zQ
kxLuUYs3feHLnL9/ljXLmPe5xvvdbKqliFqKPRkn9E0ZeZb5yXjK4xLuS3i+
kFoLaPc8cs9xlflnMNfSGafJ5J9IPydYsU/dkPDoOusK62eYyQcINtRGgeNs
PE6O/s38LrZ9Visw5VgnLLT+AAtse8Hay1h1Pt71AAqu9sKj060QQi2BxF3i
AXWEGUqINpPzJM1arl9ZjLFc2jPfjTypp4h6iryeQXDPJ/dcN3nWfCK4O8rz
WoqdzD+e/GPJP4rrPmTshrLGBxMPjLtRB+ctpx9QVJjXRIf6faTVbWN8f7U3
ltkORECIV4PGlMQo1NoNQvz59tTCNYkHZxQdfL6NZP2NvSprSSWHx+TyxFF+
pyLeDwm+Il5yFO7ZLjL3TCeZfxp/n2wjz2vxRCzjNJprRXJeCKeNQkzoe9bG
QBW6IsRwGNKc1/xmdld/Dot8gCX2fWHjflX1WbyHU3+X5LoNpdffQ9z5t/CQ
GsKoIZj5EcJcD6dPHl2WtSTw/sm0ZSp5pZNfhqPMV/AWeKxwT1dsL/gnKrYX
3EX8CPuHCf4q+9P3tFUA7xNwUUADkSbaiL61uwn3xnFVUJAPCw/DJt+re0wh
8weuo5Fq2AGx5B8hfMH+HkyEcP0w2iqS941mDMcyXxJuyPySrWVNIl+TFSQK
7sL2ljL/GIW7sH0obR9kLNte8Pfj+j68lzdt53tOfNZAnPloBHv8+3dbz7/z
VmtKDnMBHHog8WJbRHHtcMUnD87JvSTUUO7xkaxhUeQVzbiIJccYCzlWVJzV
djeXuUeI3OXvg01k2wcayrb3JX9vru/FGPbkjH37lKzlDmfVhGsTkBQT/ht/
NOb/e++I1LoTvI6j3q4HfdIKEbxHyBm5bgVSy/3zck8JJpdQ6gmjf8JNZa4R
CmcVbzMlb4XtL8mxf4+29+e1PlznDte8Te4erCVurIuuhDvr5B3ez/t0V0Td
XIbq6qo/9H8MjTXmeuuj1KInfdIeobTTfa4fQPjx3n7kEHBOtmkgfRRoIPNU
QYmXe4YyRLwL7iJehK2F3T24nhs5u7A/ObO+O7L3OrBn3TrKc0Sw0SDcc/3P
35c+r0XkSy2vz769CYXm/RD+a3sE8d4BtJ0P4Sl6Jfdep9T2k+PDR4E4vnNW
trk6XtxPyjYXXJ3I2Z7c7fmcY0tY75dhz3nO+XAL3Ls0A/l5eQ2zyB/d1NcL
32T770GppSZCT3RE4Am5N3rRjm60o8sR2X4CrsdknsLGAk5HFVsLHJY5qjnf
5Ax3k7OPFWcfCz5zWnBvuUeGz9mP4OtkouLxZ/z/SGNbRPtcQoWtNiLPdkPA
sebwJkc3cnMiL3vysiNsFdjsk3la7ZV53dgt87y+U8I1wnyHhKucQa9wFjVT
IM7LWtrA12i26u8L/ltfPK9FPdPERwYi03EhMs0GIeBwR3gyLtxoYwdythYc
BBdyNFc4CphulXBZgQmfAy7xOfPSZhlGm2SY6MvaLPe+Ba9f+8Hf0UB1vz+a
F//Xpvav+L/oh55GyLWfjETmot+Rzri191XY7ZXfSVynBjPyvUy+JoIrn8WM
9eS94c8SDDbKe8ONCvSExmaMr7fhdPAtzob9kJGa+Lvvqv9MLWLLy32CUHcj
PLb9DokmWgg+3QceBzVgu6s5LLe9iuv6zWBOH5hSy2Xa/JICcWy6+RXiDZht
ac5ntXdwc0drOO97HSFiHr0xS7X+X/23Kc/3nsrKSsSE+uCRyzHOfLpIZQ9O
uPQRws/3QuCpHvA/0QU+x97l7NwZPke7sEa8y/PdEHGhFx4asA4a9EekQS/E
GrVEvPVX9EXcX+qLF+l5Pn7FuSeZKYiP8EFsgDkSvY4hwkYPITd+QojFCoRZ
rUUM56U4P2NEBNgjJTYYyYmxSEtJwOO0pCZ/z/KyN7V//oz6KLa/+2+dxNbQ
P6lJ+Ers1X+HpUbj757//u/++6aXtf0v11tJ+g==
"], {{0, 50}, {50, 0}}, {0,
        255},
ColorFunction->RGBColor],
BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Automatic,
ImageSizeRaw->{50, 50},
PlotRange->{{0, 50}, {0, 50}}]\),
   CloudGet["https://wolfr.am/QRLuEfy7"]};

fruitroller
&#10005

fruitroller[fruits_] := With[{roll = RandomChoice[fruits, 3]},Column[{Row@roll, Which[SameQ @@ roll, Text["Winner"],DuplicateFreeQ[roll], Text["Loser"],True, Text["Try again"]]}]]

fruitroller
&#10005

fruitroller[fruits]

In a mini-project from the final week of this introductory program, participants used geographic functionality to explore the well-known traveling salesman problem by creating a map of the shortest tour connecting all African countries:

With
&#10005

With[{africa = CountryData[Entity["GeographicRegion", "Africa"]]},GeoGraphics[{Thick, Red, GeoPath@Part[africa, FindShortestTour@EntityValue[africa, "Position"] // Last]}]]

Building Skills, Exploring More Courses and Certifications

Daily Study Group sessions during the month of May were devoted to more advanced programming concepts. Wolfram certified instructor Jayanta Phadakar presented lessons on functions, expressions, patterns and package development, among other topics. The Programming Fundamentals series was our most popular Study Group, with over three thousand participants during the month. This extensive program required an extended commitment from participants, with almost 10% successfully completing assigned exercises to earn Level I Certification in Wolfram Language Programming Fundamentals.

Level I Certification in Wolfram Language Programming Fundamentals

In June and July our Study Groups branched out to dive into topics from Wolfram U interactive courses including Introduction to Notebooks, Introduction to Image Processing and Multiparadigm Data Science. Wolfram U course authors and veteran instructors Dave Withoff and Abrita Chakravarty provided insights from their courses and encouraged everyone to take the full interactive courses and pursue the certifications available there.

This Study Group represented an interesting mix of members, attracting more academic and business professionals and fewer students than our previous groups:

Which best describes you?

We were impressed by the interaction among the diverse participants, who learned a lot by helping each other work through problems. Many attendees agreed that these informal discussions taking place on Wolfram Community and in the Study Group chat provided invaluable perspective that helped them further solidify their understanding of the concepts.

Special-Interest Study Groups: Mathematics, Modeling and Analysis

The remainder of the 2020 Daily Study Groups have been devoted to specific topics in mathematics, modeling and COVID-19 data analysis. The three-week calculus group was scheduled just prior to the start of the new school year in August and proved to be our second most popular group. Many group members were interested to learn calculus functionality, of course, but others used the Study Group to explore teaching techniques and methods for supporting their students.

What is your primary motivation for attending this calculus Study Group?

Our linear algebra Study Group just wrapped at the end of October, advancing our progression of mathematics topics. We hope to cover more math material in future sessions. (Until then, check out self-study math courses from Wolfram U.)

System modeling was the focus of another Study Group in September. We were surprised to see in our first-day poll that 87% of the group entered with little to no prior knowledge of the subject:

How familiar are you with modeling?

The challenge for our instructors was to offer a full range of examples and topics to cater to different interests and experience levels. Their efforts paid off; at the end of the weeklong program, our poll showed that every category was useful to at least some of our participants:

Which topics from this Study Group were most useful to you?

Our subsequent data analysis Study Group focused on computations using publicly available COVID-19 epidemic data from the Wolfram Data Repository. This Study Group expanded on the fast-paced lessons from the similarly named Wolfram U video course, taking time to explain concepts and field questions from the group.

Video course

Up Next: Machine Learning… Then Start Again!

Heading into the final two months of the year, we have time to squeeze in a couple more Daily Study Groups. We’re having too much fun to stop now!

Machine learning in the Wolfram Language is a topic that is in high demand, and we have plans for two new groups. The first will spend a week in November covering machine learning basics such as supervised and unsupervised learning, neural networks and the built-in machine learning functions in the Wolfram Language. The second group will follow this introductory week and will feature explorations in biodiversity using machine learning.

We’ll continue Daily Study Groups in 2021, starting fresh with a reprise of introductory Wolfram Language topics. We’re also planning to explore bundles of the beautiful new workflows featured in Wolfram Language documentation on topics from data analysis to API deployment, as well as the tremendous catalog of training material in our Wolfram U archives. Visit Wolfram U to browse our collection of self-directed courses and available certifications.

With all this new material, we have a little something for everyone. So sign up for one of our upcoming Daily Study Groups, check out the archived content from our previous sessions and let us know if you have any suggestions for topics. We hope to see you soon—and until then, never stop learning!


Special Thanks

At Wolfram, we’re fortunate to be surrounded by colleagues with specialized fields of interests and experience in academia and teaching. We’re thankful for all the Study Group instructors and teaching assistants who have helped us to provide such a rich resource to so many, and we’re inspired by the folks from all sorts of backgrounds, from all around the world, who have participated in Daily Study Groups. In short, the secret to the success of Wolfram Daily Study Groups comes down to a combination of talented instructors, reliable event management and the power of the Wolfram Language. Running a daily online program is a big task and requires much coordination and teamwork. My thanks go to Cassidy Hinkle, technical project manager for Wolfram U, and all the instructors and teaching assistants who helped make Daily Study Groups a reality.

Check out Wolfram U for a wealth of free interactive courses, video courses and special events.

Leave a Comment

No Comments




Leave a comment