danjenkins,
As it happens I was asked a few months ago to specify a system for Matlab, flight dynamics problems. That system had fast, dual 8-core Xeons, 128GB of RAM, a large PCIe SSD main drive and would have cost about $12,000 range. My friend instead contracted the work!
Most custom algorithmic programs are completely multi-threaded and so can use all the available threads full bore and cab benefit from co-processors such as NVIDIA Tesla and Xeon Phi. As extreme precision is necessary due to the possibility of compounded errors, it's essential in my view to use ECC error-correcting RAM. If there will be 3D simulations a very fast graphics card with a wide bandwidth and lot of memory is desirable, but if it's numbers, a strong 2D performance is all that's necessary.
The following system idea is what I would describe as a minimalist system for this kind of work in that it is 4-core and limited to 32GB. Also, as a LGA1150 / Xeon E3, the memory bandwidth and PCIe lanes are limited as compared to LGA2011 / Xeon E5, which would be my preference. LGA2011 may also be upgraded in future to 6, 8, 10, 12, 14, and even 18 cores.
Ideally, giving the possibility of large, complex problems as time progresses, I would suggest a system having a dual LGA2011 (or the new LGA2011-3) motherboard, starting with a single 6-core Xeon E5-2XXX-eries CPU and 32GB RAM and then adding the second CPU and another 32GB later. However, the starting point would be $2500 or more. a medium solution would use a single Xeon E5-1600 series like the excellent 6-core E5-1650 V2 -or V3 if it's LGA2011-3 and that CPU could be changed for a 10 -core later.
Anyway, here are a couple of system ideas:
BambiBoom PixelCannon Cadamodarendergrapharific iWork TurboBlast ExtremeSignature SuperModel 8000 ®©$$™®£™©™_ 10.8.14
1. Intel Xeon E5-1630 v3 Quad-Core Processor 3.7 / 3.8GHz 0GT/s 10MB LGA 2011-v3 CPU, OEM > $380
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http://ark.intel.com/products/82764/Intel-Xeon-Processor-E5-1630-v3-10M-Cache-3_70-GHz?q=e5-1630
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http://www.superbiiz.com/detail.php?name=E5-1630V3
2. Cooler Master Hyper 212 EVO CPU Fan For Intel LGA1366/1156/1155/1150/775 & AMD FM1/AM3+/AM3/AM2+/AM2 > $31.
3. Motherboard: ASRock X99 Extreme4 LGA 2011-v3 Intel X99 SATA 6Gb/s USB 3.0 ATX Intel Motherboard > $240
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http://www.newegg.com/Product/Product.aspx?Item=N82E16813157543&cm_re=asrock_x99_extreme_4-_-13-157-543-_-Product
4. Crucial 16GB (2 x 8GB) 288-Pin DDR4 SDRAM ECC DDR4 2133 (PC4-17000) Server Memory Model CT2K8G4RFS4213 > $244
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http://www.newegg.com/Product/Product.aspx?Item=N82E16820148839&cm_re=Crucial_16GB_%282_x_8GB%29_288-Pin_DDR4_SDRAM_ECC_DDR4_2133_%28PC4-17000%29_Server_Memory-_-20-148-839-_-Product
5. GPU: PNY NVIDIA Quadro K620 2GB DDR3 DVI/DisplayPort Low Profile PCI-Express Video Card> $169.
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http://www.superbiiz.com/detail.php?name=PNY-K620G2
6. Crucial MX100 CT256MX100SSD1 2.5" 256GB SATA III MLC Internal Solid State Drive (SSD) ) > $113 (OS, applications, working files)
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http://www.newegg.com/Product/Product.aspx?Item=N82E16820148820&cm_re=crucial_mx110-_-20-148-820-_-Product
7. Western Digital Caviar Black WD1002FAEX 1TB 7200RPM SATA3/SATA 6.0 GB/s 64MB Hard Drive > $82 (Files, Backup, System Image)
8. CORSAIR HX Series HX750 750W ATX12V 2.3 / EPS12V 2.91 SLI CrossFire 80 PLUS GOLD Certified Modular Active PFC Power Supply New 4th Gen CPU Certified Haswell Ready> $130
9. Samsung SH-224DB/BEBE 24X SATA DVD±RW Internal Drive w/o Software (Black) SH-224DB $17.99
10. LIAN LI PC-A75X No Power Supply ATX Full Tower Case (Black) CA-A75 $170
11. Microsoft Windows 7 Professional 64-bit w/ SP1 (1-Pack, DVD), OEM MSFQC04649 $138.99
12. Monitor: Dell 469-4320 24 inch Widescreen 1,000:1 5ms VGA/DVI LED LCD Monitor (Black) > $168
http://www.superbiiz.com/detail.php?name=DEL-E2414H
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TOTAL = $ 1886
This is about +$400 your budget, but I think a very good performing, and forward-looking solution that might delay changing the entire system an extra 2-3 years- last through graduate school?
If you are quite strict about the budget and the expectation for upgrades and expansion are modest:
BambiBoom Mathalabacalcurific WalletJoyScream Turbosignature 9000 $$©& £℞™_10.23.14
CPU: Intel Xeon E3-1246 v3 Quad-Core Processor 3.5 / 3.9GHz 5.0GT/s 8MB LGA 1150 CPU >$278
http://ark.intel.com/products/80916/Intel-Xeon-Processor-E3-1246-v3-8M-Cache-3_50-GHz
http://www.superbiiz.com/detail.php?name=E3-1246V3B
CPU Cooler: Cooler Master Hyper 212 EVO - CPU Cooler with 120 mm PWM Fan > $40
Motherboard: Asus P9D-X LGA1150/ Intel C222/ DDR3/ SATA3&USB3.0/ V&2GbE/ ATX Server Motherboard > $169
http://www.superbiiz.com/detail.php?name=MB-P9D-X
Memory: 16GB (2) Samsung DDR3-1600 8GB/1Gx72 ECC CL11 Server Memory > $180 ($90 ea)
http://www.superbiiz.com/detail.php?name=D38GRE160S
GPU: PNY NVIDIA Quadro K620 2GB DDR3 DVI/DisplayPort Low Profile PCI-Express Video Card> $169.
http://www.superbiiz.com/detail.php?name=PNY-K620G2
PSU: CORSAIR CXM series CX600M 600W ATX12V v2.3 SLI CrossFire 80 PLUS BRONZE Certified Modular Active PFC Power Supply > $70.
Crucial MX100 CT256MX100SSD1 2.5" 256GB SATA III MLC Internal Solid State Drive (SSD) > $113 (Newegg)
Western Digital WD Blue WD10EZEX 1TB 7200 RPM 64MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive Bare Drive - OEM > $60
Optical Drive: Samsung SH-224DB/BEBE 24X SATA DVD±RW Internal Drive w/o Software (Black) > $18
Case: LIAN LI PC-9NB Black Aluminum ATX Mid Tower Computer Case > $100
Operating System: Microsoft Windows 7 Professional SP1 64-bit - OEM > $138
Monitor: Dell 469-4320 24 inch Widescreen 1,000:1 5ms VGA/DVI LED LCD Monitor (Black) > $168
http://www.superbiiz.com/detail.php?name=DEL-E2414H
TOTAL = $1503.
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So, a couple of configurations to consider.
Another possibility, with some risks, but also some potentially good rewards would be to consider a used Dell Precision T7500 with a pair of the excellent Xeon X5680 six-core CPU's @ 3.33 / 3.6GHz- that's 12-cores /24 threads, and then revise as neceaaary. these are often seen with 48GB RAM and sometimes very goof graphics cards. A completed sale on Ebahhh:
http://www.ebay.com/itm/Dell-Precision-T7500-PC-2X-3-33GHz-X5680-Xeon-Hex-16GB-RAM-4X-HDD-Win-7-Ult-/171413374055?pt=Desktop_PCs&hash=item27e9088467
-with 16GB RAM sold for $1176. the 2GB Firepro V7800 GPU is probably excess to need. So, add the monitor and another 24GB RAM (= +3 X 8GB, the X58 chipset adds RAM in sets of 3 modules), possibly a Tesla co-precessor in future- these are very reasonably priced used and this would have have a very high capability close or within your budget, without researching, ordering, assembling, configuring, testing, trouble-shooting a new system. This system would have cost $7,000+ new. No guarantees, but I'll mention that I bought a used, dual Xeon Dell Precision in 2010 and it's run for 4 years usually on 20 hours per day and without a single failure.
Cheers,
BambiBoom
HP z420 (2014) > Xeon E5-1620 quad core @ 3.6 / 3.8GHz > 24GB DDR3 ECC 1600 RAM > Quadro 4000 (2GB)> Samsung 840 SSD 250GB /Western Digital Black WD1003FZEX 1TB> M-Audio 192 sound card > AE3000 USB WiFi > HP 2711X, 27" 1920 X 1080 > Windows 7 Ultimate 64 >[Passmark system rating = 3923, CPU= 9223/ 2D= 839 / 3D=2048]
Dell Precision T5400 (2008) > 2X Xeon X5460 quad core @3.16GHz > 16GB DDR2 ECC 667> Quadro FX 4800 (1.5GB) > WD RE4 500GB / Seagate Barracuda 500GB > M-Audio 2496 Sound Card / Linksys 600N WiFi > Dell 24" and Dell 19" LCD > Windows 7 Ultimate 64-bit > [Passmark system rating = 1859, CPU = 8528 / 2D= 512 / 3D=1097]
Dell Precision 390 (2005) Xeon x3230 quad core @ 2.67GHz > 6 GB DDR2 ECC 667 > Firepro V4900 (1GB)> 2X WD 320GB > 2X Dell 19" LCD > Windows 7 Professional 64-bit [Passmark system rating = 1431, CPU = 3642 / 2D= 433 / 3D=1346]
2D, 3D CAD, Image Processing, Rendering, Text > Architecture, industrial design, graphic design, written projects